Jean-Pierre Serre: Difference between revisions
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| name = Jean-Pierre Serre |
| name = Jean-Pierre Serre |
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| image = Jean-Pierre Serre 2003.jpg |
| image = Jean-Pierre Serre 2003.jpg |
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| caption = |
| caption = Serre in 2003 |
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| birth_date = {{Birth date and age|df=y|1926|09|15}} |
| birth_date = {{Birth date and age|df=y|1926|09|15}} |
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| birth_place = [[Bages, Pyrénées-Orientales|Bages]], [[Pyrénées-Orientales]], |
| birth_place = [[Bages, Pyrénées-Orientales|Bages]], [[Pyrénées-Orientales]], France |
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| field = [[Mathematics]] |
| field = [[Mathematics]] |
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| work_institutions = {{plainlist| |
| work_institutions = {{plainlist| |
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*[[Centre National de la Recherche Scientifique]] |
*[[Centre National de la Recherche Scientifique]] |
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'''Jean-Pierre Serre''' ({{IPA |
'''Jean-Pierre Serre''' ({{IPA|fr|sɛʁ|lang}}; born 15 September 1926) is a French [[mathematician]] who has made contributions to [[algebraic topology]], [[algebraic geometry]] and [[algebraic number theory]]. He was awarded the [[Fields Medal]] in 1954, the [[Wolf Prize]] in 2000 and the inaugural [[Abel Prize]] in 2003. |
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==Biography== |
==Biography== |
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===Personal life=== |
===Personal life=== |
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Born in [[Bages, Pyrénées-Orientales|Bages]], [[Pyrénées-Orientales |
Born in [[Bages, Pyrénées-Orientales|Bages]], [[Pyrénées-Orientales]], to pharmacist parents, Serre was educated at the Lycée de Nîmes. Then he studied at the [[École Normale Supérieure]] in [[Paris]] from 1945 to 1948.<ref>J J O'Connor and E F Robertson ''Serre Biography'' http://www-history.mcs.st-andrews.ac.uk/Biographies/Serre.html</ref> He was awarded his doctorate from the [[University of Paris|Sorbonne]] in 1951. From 1948 to 1954 he held positions at the [[Centre National de la Recherche Scientifique]] in [[Paris]]. In 1956 he was elected professor at the [[Collège de France]], a position he held until his retirement in 1994. |
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His wife, Professor Josiane Heulot-Serre, was a chemist; she also was the director of the Ecole Normale Supérieure de Jeunes Filles. Their daughter is the former French diplomat, historian and writer [[Claudine Monteil]]. The French mathematician [[Denis Serre]] is his nephew. He practices skiing, table tennis, and rock climbing (in [[Fontainebleau]]). |
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===Career=== |
===Career=== |
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From a very young age he was an outstanding figure in the school of [[Henri Cartan]],<ref>{{Cite journal | last1 = Serre | first1 = J. -P. | author-link=Jean-Pierre Serre| doi = 10.1098/rsbm.2009.0005 | title = Henri Paul Cartan. 8 July 1904 -- 13 August 2008 | journal = [[Biographical Memoirs of Fellows of the Royal Society]] | volume = 55 | pages = 37–44 | year = 2009 | title-link = Henri Cartan | doi-access = |
From a very young age he was an outstanding figure in the school of [[Henri Cartan]],<ref>{{Cite journal | last1 = Serre | first1 = J. -P. | author-link=Jean-Pierre Serre| doi = 10.1098/rsbm.2009.0005 | title = Henri Paul Cartan. 8 July 1904 -- 13 August 2008 | journal = [[Biographical Memoirs of Fellows of the Royal Society]] | volume = 55 | pages = 37–44 | year = 2009 | title-link = Henri Cartan | doi-access = }}</ref> working on [[algebraic topology]], [[several complex variables]] and then [[commutative algebra]] and [[algebraic geometry]], where he introduced [[sheaf (mathematics)|sheaf]] theory and [[homological algebra]] techniques. Serre's thesis concerned the [[Serre spectral sequence|Leray–Serre spectral sequence]] associated to a [[fibration]]. Together with Cartan, Serre established the technique of using [[Eilenberg–MacLane space]]s for computing [[homotopy groups of spheres]], which at that time was one of the major problems in topology. |
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In his speech at the Fields Medal award ceremony in 1954, [[Hermann Weyl]] gave high praise to Serre, and also made the point that the award was for the first time awarded to a non-analyst. Serre subsequently changed his research focus. |
In his speech at the Fields Medal award ceremony in 1954, [[Hermann Weyl]] gave high praise to Serre, and also made the point that the award was for the first time awarded to a non-analyst. Serre subsequently changed his research focus. |
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====Algebraic geometry==== |
====Algebraic geometry==== |
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In the 1950s and 1960s, a fruitful collaboration between Serre and the two-years-younger [[Alexander Grothendieck]] led to important foundational work, much of it motivated by the [[Weil conjectures]]. Two major foundational papers by Serre were ''Faisceaux Algébriques Cohérents'' (FAC, 1955),<ref>{{cite journal | last1 = Serre | first1 = Jean-Pierre | year = 1955 | title = Faisceaux Algébriques Cohérents | journal = The Annals of Mathematics | volume = 61 | issue = 2| pages = 197–278 | doi=10.2307/1969915| jstor = 1969915 }}</ref> on [[coherent cohomology]], and ''Géométrie Algébrique et Géométrie Analytique'' ([[GAGA]], 1956).<ref>{{Citation | last1=Serre | first1=Jean-Pierre | author1-link=Jean-Pierre Serre | title=Géométrie algébrique et géométrie analytique | url=http://www.numdam.org/numdam-bin/item?id=AIF_1956__6__1_0 | mr=0082175 | year=1956 | journal=[[Annales de l'Institut Fourier]] | issn=0373-0956 | volume=6 | pages=1–42 | doi=10.5802/aif.59| doi-access=free }}</ref> |
In the 1950s and 1960s, a fruitful collaboration between Serre and the two-years-younger [[Alexander Grothendieck]] led to important foundational work, much of it motivated by the [[Weil conjectures]]. Two major foundational papers by Serre were ''Faisceaux Algébriques Cohérents'' (FAC, 1955),<ref name="Serre FAC 1955">{{cite journal | last1 = Serre | first1 = Jean-Pierre | year = 1955 | title = Faisceaux Algébriques Cohérents | journal = The Annals of Mathematics | volume = 61 | issue = 2| pages = 197–278 | doi=10.2307/1969915| jstor = 1969915 }}</ref> on [[coherent cohomology]], and ''Géométrie Algébrique et Géométrie Analytique'' ([[GAGA]], 1956).<ref>{{Citation | last1=Serre | first1=Jean-Pierre | author1-link=Jean-Pierre Serre | title=Géométrie algébrique et géométrie analytique | url=http://www.numdam.org/numdam-bin/item?id=AIF_1956__6__1_0 | mr=0082175 | year=1956 | journal=[[Annales de l'Institut Fourier]] | issn=0373-0956 | volume=6 | pages=1–42 | doi=10.5802/aif.59| doi-access=free }}</ref> |
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Even at an early stage in his work Serre had perceived a need to construct more general and refined [[cohomology]] theories to tackle the Weil conjectures. The problem was that the cohomology of a [[coherent sheaf]] over a [[finite field]] could not capture as much topology as [[singular cohomology]] with integer coefficients. Amongst Serre's early candidate theories of 1954–55 was one based on [[Witt vector]] coefficients. |
Even at an early stage in his work Serre had perceived a need to construct more general and refined [[cohomology]] theories to tackle the Weil conjectures. The problem was that the cohomology of a [[coherent sheaf]] over a [[finite field]] could not capture as much topology as [[singular cohomology]] with integer coefficients. Amongst Serre's early candidate theories of 1954–55 was one based on [[Witt vector]] coefficients. |
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Amongst his most original contributions were: his "[[Serre's conjecture II (algebra)|Conjecture II]]" (still open) on Galois cohomology; his use of [[group action (mathematics)|group actions]] on [[Bass–Serre theory|trees]] (with [[Hyman Bass]]); the Borel–Serre compactification; results on the number of points of curves over finite fields; [[Galois representation]]s in [[l-adic cohomology|ℓ-adic cohomology]] and the proof that these representations have often a "large" image; the concept of [[p-adic modular form]]; and the [[Serre conjecture (number theory)|Serre conjecture]] (now a theorem) on mod-''p'' representations that made [[Fermat's Last Theorem]] a connected part of mainstream [[arithmetic geometry]]. |
Amongst his most original contributions were: his "[[Serre's conjecture II (algebra)|Conjecture II]]" (still open) on Galois cohomology; his use of [[group action (mathematics)|group actions]] on [[Bass–Serre theory|trees]] (with [[Hyman Bass]]); the Borel–Serre compactification; results on the number of points of curves over finite fields; [[Galois representation]]s in [[l-adic cohomology|ℓ-adic cohomology]] and the proof that these representations have often a "large" image; the concept of [[p-adic modular form]]; and the [[Serre conjecture (number theory)|Serre conjecture]] (now a theorem) on mod-''p'' representations that made [[Fermat's Last Theorem]] a connected part of mainstream [[arithmetic geometry]]. |
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In his paper FAC, Serre asked whether a finitely generated [[projective module]] over a [[polynomial ring]] is [[free module|free]]. This question led to a great deal of activity in [[commutative algebra]], and was finally answered in the affirmative by [[Daniel Quillen]] and [[Andrei Suslin]] independently in 1976. This result is now known as the [[Quillen–Suslin theorem]]. |
In his paper FAC,<ref name="Serre FAC 1955" /> Serre asked whether a finitely generated [[projective module]] over a [[polynomial ring]] is [[free module|free]]. This question led to a great deal of activity in [[commutative algebra]], and was finally answered in the affirmative by [[Daniel Quillen]] and [[Andrei Suslin]] independently in 1976. This result is now known as the [[Quillen–Suslin theorem]]. |
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==Honors and awards== |
==Honors and awards== |
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Serre, at twenty-seven in 1954, was and still is the youngest person ever to have been awarded the [[Fields Medal]]. He went on to win the [[Balzan Prize]] in 1985, the [[Steele Prize]] in 1995, the [[Wolf Prize in Mathematics]] in 2000, and was the first recipient of the [[Abel Prize]] in 2003. He has been awarded other prizes, such as the Gold Medal of the French National Scientific Research Centre (Centre National de la Recherche Scientifique, CNRS). |
Serre, at twenty-seven in 1954, was and still is the youngest person ever to have been awarded the [[Fields Medal]]. He went on to win the [[Balzan Prize]] in 1985, the [[Steele Prize]] in 1995, the [[Wolf Prize in Mathematics]] in 2000, and was the first recipient of the [[Abel Prize]] in 2003. He has been awarded other prizes, such as the Gold Medal of the French National Scientific Research Centre (Centre National de la Recherche Scientifique, CNRS). |
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He is a foreign member of several scientific Academies ( |
He is a foreign member of several scientific Academies (US, Norway, Sweden, Russia, the Royal Society, [[Royal Netherlands Academy of Arts and Sciences]] (1978),<ref>{{cite web |url=https://www.knaw.nl/en/members/foreign-members/4781 |title=J.-P. Serre |publisher=Royal Netherlands Academy of Arts and Sciences |access-date=4 August 2015 |archive-date=5 March 2016 |archive-url=https://web.archive.org/web/20160305010020/https://www.knaw.nl/en/members/foreign-members/4781 |url-status=dead }}</ref> [[American Academy of Arts and Sciences]],<ref>{{Cite web|title=Jean-Pierre Serre|url=https://www.amacad.org/person/jean-pierre-serre|access-date=2021-12-02|website=American Academy of Arts & Sciences|language=en}}</ref> [[National Academy of Sciences]],<ref>{{Cite web|title=Jean-Pierre Serre|url=http://www.nasonline.org/member-directory/members/45913.html|access-date=2021-12-02|website=www.nasonline.org}}</ref> the [[American Philosophical Society]]<ref>{{Cite web|title=APS Member History|url=https://search.amphilsoc.org/memhist/search?creator=Jean-Pierre+Serre&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced|access-date=2021-12-02|website=search.amphilsoc.org}}</ref>) and has received many honorary degrees (from Cambridge, Oxford, Harvard, Oslo and others). In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-07-18.</ref> |
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Serre has been awarded the highest honors in France as [[Legion of Honour|Grand Cross of the Legion of Honour]] (Grand Croix de la Légion d'Honneur) and [[Ordre national du Mérite|Grand Cross of the Legion of Merit]] (Grand Croix de l'Ordre National du Mérite). |
Serre has been awarded the highest honors in France as [[Legion of Honour|Grand Cross of the Legion of Honour]] (Grand Croix de la Légion d'Honneur) and [[Ordre national du Mérite|Grand Cross of the Legion of Merit]] (Grand Croix de l'Ordre National du Mérite). |
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==See also== |
==See also== |
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* [[Multiplicity (mathematics)]] |
* [[Multiplicity (mathematics)]] |
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* [[Bourbaki group]] — Serre joined it in the late 1940s |
* [[Bourbaki group]] — Serre joined it in the late 1940s |
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*''Algèbre Locale, Multiplicités'' (1965) Collège de France course 1957–58, as |
*''Algèbre Locale, Multiplicités'' (1965) Collège de France course 1957–58, as |
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**{{cite book |doi=10.1007/978-3-662-04203-8|title=Local Algebra|series=Springer Monographs in Mathematics|year=2000|isbn=978-3-642-08590-1}} |
**{{cite book |doi=10.1007/978-3-662-04203-8|title=Local Algebra|series=Springer Monographs in Mathematics|year=2000|isbn=978-3-642-08590-1}} |
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*{{cite book |doi=10.1007/978-3-540-70634-2|title=Lie Algebras and Lie Groups|series=Lecture Notes in Mathematics|year=1992|volume=1500|isbn=978-3-540-55008-2}} |
*{{cite book |doi=10.1007/978-3-540-70634-2|title=Lie Algebras and Lie Groups|series=Lecture Notes in Mathematics|year=1992|volume=1500|isbn=978-3-540-55008-2 }} |
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*''Algèbres de Lie Semi-simples Complexes'' (1966), as |
*''Algèbres de Lie Semi-simples Complexes'' (1966), as |
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**{{cite book |doi=10.1007/978-1-4757-3910-7|title=Complex Semisimple Lie Algebras|year=1987|last1=Serre|first1=Jean-Pierre|isbn=978-0-387-96569-7}} |
**{{cite book |doi=10.1007/978-1-4757-3910-7|title=Complex Semisimple Lie Algebras|year=1987|last1=Serre|first1=Jean-Pierre|isbn=978-0-387-96569-7}} |
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**{{cite book |doi=10.1007/978-3-642-61856-7|title=Trees|year=1980|last1=Serre|first1=Jean-Pierre|isbn=978-3-642-61858-1}}<ref>{{cite journal|author=Alperin, Roger C.|author-link=Roger C. Alperin|title=Review: ''Group, trees and projective modules'', by Warren Dicks; and ''Trees'', by Jean-Pierre Serre|journal=Bull. Amer. Math. Soc. (N.S.)|year=1983|volume=8|issue=2|pages=401–405|url=https://www.ams.org/journals/bull/1983-08-02/S0273-0979-1983-15146-7/S0273-0979-1983-15146-7.pdf|doi=10.1090/s0273-0979-1983-15146-7|doi-access=free}}</ref> |
**{{cite book |doi=10.1007/978-3-642-61856-7|title=Trees|year=1980|last1=Serre|first1=Jean-Pierre|isbn=978-3-642-61858-1}}<ref>{{cite journal|author=Alperin, Roger C.|author-link=Roger C. Alperin|title=Review: ''Group, trees and projective modules'', by Warren Dicks; and ''Trees'', by Jean-Pierre Serre|journal=Bull. Amer. Math. Soc. (N.S.)|year=1983|volume=8|issue=2|pages=401–405|url=https://www.ams.org/journals/bull/1983-08-02/S0273-0979-1983-15146-7/S0273-0979-1983-15146-7.pdf|doi=10.1090/s0273-0979-1983-15146-7|doi-access=free}}</ref> |
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*''Oeuvres/Collected Papers in four volumes'' (1986) Vol. IV in 2000, Springer-Verlag |
*''Oeuvres/Collected Papers in four volumes'' (1986) Vol. IV in 2000, Springer-Verlag |
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**{{cite book |isbn=978-3-642-39815-5|title=Oeuvres - Collected Papers I: 1949 - 1959|last1=Serre|first1=Jean-Pierre|date=2 December 2013}} |
**{{cite book |isbn=978-3-642-39815-5|title=Oeuvres - Collected Papers I: 1949 - 1959|last1=Serre|first1=Jean-Pierre|date=2 December 2013|publisher=Springer }} |
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**{{cite book |isbn=978-3-642-37725-9|title=Oeuvres - Collected Papers II: 1960 - 1971|last1=Serre|first1=Jean-Pierre|date=4 December 2013}} |
**{{cite book |isbn=978-3-642-37725-9|title=Oeuvres - Collected Papers II: 1960 - 1971|last1=Serre|first1=Jean-Pierre|date=4 December 2013|publisher=Springer }} |
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**{{cite book |isbn=978-3-642-39837-7|title=Oeuvres - Collected Papers III: 1972 - 1984|last1=Serre|first1=Jean-Pierre|date=14 April 2014}} |
**{{cite book |isbn=978-3-642-39837-7|title=Oeuvres - Collected Papers III: 1972 - 1984|last1=Serre|first1=Jean-Pierre|date=14 April 2014|publisher=Springer }} |
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**{{cite book |isbn=978-3-642-39839-1|title=Oeuvres - Collected Papers IV: 1985 - 1998|last1=Serre|first1=Jean-Pierre|date=19 December 2013}} |
**{{cite book |isbn=978-3-642-39839-1|title=Oeuvres - Collected Papers IV: 1985 - 1998|last1=Serre|first1=Jean-Pierre|date=19 December 2013|publisher=Springer }} |
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*{{cite book |doi=10.1007/978-3-663-10632-6|title=Lectures on the Mordell-Weil Theorem|series=Aspects of Mathematics|year=1997|volume=15|isbn=978-3-663-10634-0}} |
*{{cite book |doi=10.1007/978-3-663-10632-6|title=Lectures on the Mordell-Weil Theorem|series=Aspects of Mathematics|year=1997|volume=15|isbn=978-3-663-10634-0}} |
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*{{cite book |doi=10.1201/b10588|title=Topics in Galois Theory|year=2016|last1=Serre|first1=Jean-Pierre|isbn=9780429064401}}<ref>{{cite journal|author=Fried, Michael|title=Review: ''Topics in Galois Theory'', by J.-P. Serre|journal=Bull. Amer. Math. Soc. (N.S.)|year=1994|issue=1|pages=124–135|url=https://www.ams.org/journals/bull/1994-30-01/S0273-0979-1994-00445-8/S0273-0979-1994-00445-8.pdf|doi=10.1090/S0273-0979-1994-00445-8|volume=30|doi-access=free}}</ref> |
*{{cite book |doi=10.1201/b10588|title=Topics in Galois Theory|year=2016|last1=Serre|first1=Jean-Pierre|isbn=9780429064401}}<ref>{{cite journal|author=Fried, Michael|title=Review: ''Topics in Galois Theory'', by J.-P. Serre|journal=Bull. Amer. Math. Soc. (N.S.)|year=1994|issue=1|pages=124–135|url=https://www.ams.org/journals/bull/1994-30-01/S0273-0979-1994-00445-8/S0273-0979-1994-00445-8.pdf|doi=10.1090/S0273-0979-1994-00445-8|volume=30|doi-access=free}}</ref> |
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* ''Exposés de séminaires 1950–1999 '' (2001), SMF, {{isbn|9782856291030}},{{isbn|9782856292426}} |
* ''Exposés de séminaires 1950–1999 '' (2001), SMF, {{isbn|9782856291030}},{{isbn|9782856292426}} |
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*{{cite book |isbn=978-1-4704-2174-8|title=Cohomological Invariants in Galois Cohomology|last1=Garibaldi|first1=Skip|last2=Merkurjev|first2=Alexander|last3=Serre|first3=Jean-Pierre|year=2003}} |
*{{cite book |isbn=978-1-4704-2174-8|title=Cohomological Invariants in Galois Cohomology|last1=Garibaldi|first1=Skip|last2=Merkurjev|first2=Alexander|last3=Serre|first3=Jean-Pierre|year=2003|publisher=American Mathematical Society }} |
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*{{cite book |isbn=978-0-8218-3424-4|title=Grothendieck-Serre Correspondence|last1=Grothendieck|first1=Alexandre|last2=Colmez|first2=Pierre|year=2004}} |
*{{cite book |isbn=978-0-8218-3424-4|title=Grothendieck-Serre Correspondence|last1=Grothendieck|first1=Alexandre|last2=Colmez|first2=Pierre|year=2004|publisher=American Mathematical Soc. }} |
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*{{cite book |doi=10.1201/b11315|title=Lectures on N_X(p)|year=2016|last1=Serre|first1=Jean-Pierre|isbn=9780429067617}} |
*{{cite book |doi=10.1201/b11315|title=Lectures on N_X(p)|year=2016|last1=Serre|first1=Jean-Pierre|isbn=9780429067617}} |
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* ''Correspondance Serre-Tate '' (2015), edited with [[Pierre Colmez]], SMF, {{isbn|9782856298022}} |
* ''Correspondance Serre-Tate '' (2015), edited with [[Pierre Colmez]], SMF, {{isbn|9782856298022}} |
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* ''Finite Groups: an Introduction'' (2016), Higher Education Press & International Press, {{isbn|9781571463272}} |
* ''Finite Groups: an Introduction'' (2016), Higher Education Press & International Press, {{isbn|9781571463272}} |
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* ''Rational Points on Curves over Finite Fields'' (2020), with contributions by [[E. Howe]], [[J. Oesterlé]], [[C. Ritzenthaler]], SMF, {{isbn|9782856299234}} |
* ''Rational Points on Curves over Finite Fields'' (2020), with contributions by [[E. Howe]], [[Joseph Oesterlé|J. Oesterlé]], [[C. Ritzenthaler]], SMF, {{isbn|9782856299234}} |
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{{refend}} |
{{refend}} |
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A list of corrections, and updating, of these books can be found on his home page at Collège de France. |
A [https://www.college-de-france.fr/media/jean-pierre-serre/UPL5190088847250963678%20Corrections%20to%20Serre%20books%202019.pdf list of corrections], and updating, of these books can be found on his home page at Collège de France. |
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==Notes== |
==Notes== |
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[[Category:Fields Medalists]] |
[[Category:Fields Medalists]] |
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[[Category:Academic staff of the Collège de France]] |
[[Category:Academic staff of the Collège de France]] |
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[[Category:Foreign |
[[Category:Foreign members of the Royal Society]] |
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[[Category: |
[[Category:French number theorists]] |
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[[Category:Topologists]] |
[[Category:Topologists]] |
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[[Category:University of Paris alumni]] |
[[Category:University of Paris alumni]] |
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[[Category:Grand |
[[Category:Grand Cross of the Legion of Honour]] |
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[[Category:Wolf Prize in Mathematics laureates]] |
[[Category:Wolf Prize in Mathematics laureates]] |
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[[Category:Members of the French Academy of Sciences]] |
[[Category:Members of the French Academy of Sciences]] |
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[[Category:Members of the Norwegian Academy of Science and Letters]] |
[[Category:Members of the Norwegian Academy of Science and Letters]] |
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[[Category:Members of the Royal Netherlands Academy of Arts and Sciences]] |
[[Category:Members of the Royal Netherlands Academy of Arts and Sciences]] |
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[[Category:Foreign |
[[Category:Foreign members of the Russian Academy of Sciences]] |
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[[Category:Fellows of the American Mathematical Society]] |
[[Category:Fellows of the American Mathematical Society]] |
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[[Category:Institute for Advanced Study visiting scholars]] |
[[Category:Institute for Advanced Study visiting scholars]] |
Latest revision as of 11:27, 21 October 2024
Jean-Pierre Serre | |
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Born | Bages, Pyrénées-Orientales, France | 15 September 1926
Alma mater | |
Known for | (List of things named after Jean-Pierre Serre) |
Awards |
|
Scientific career | |
Fields | Mathematics |
Institutions | |
Thesis | Homologie singulière des espaces fibrés (1951) |
Doctoral advisor | Henri Cartan |
Doctoral students |
Jean-Pierre Serre (French: [sɛʁ]; born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the inaugural Abel Prize in 2003.
Biography
[edit]Personal life
[edit]Born in Bages, Pyrénées-Orientales, to pharmacist parents, Serre was educated at the Lycée de Nîmes. Then he studied at the École Normale Supérieure in Paris from 1945 to 1948.[1] He was awarded his doctorate from the Sorbonne in 1951. From 1948 to 1954 he held positions at the Centre National de la Recherche Scientifique in Paris. In 1956 he was elected professor at the Collège de France, a position he held until his retirement in 1994.
His wife, Professor Josiane Heulot-Serre, was a chemist; she also was the director of the Ecole Normale Supérieure de Jeunes Filles. Their daughter is the former French diplomat, historian and writer Claudine Monteil. The French mathematician Denis Serre is his nephew. He practices skiing, table tennis, and rock climbing (in Fontainebleau).
Career
[edit]From a very young age he was an outstanding figure in the school of Henri Cartan,[2] working on algebraic topology, several complex variables and then commutative algebra and algebraic geometry, where he introduced sheaf theory and homological algebra techniques. Serre's thesis concerned the Leray–Serre spectral sequence associated to a fibration. Together with Cartan, Serre established the technique of using Eilenberg–MacLane spaces for computing homotopy groups of spheres, which at that time was one of the major problems in topology.
In his speech at the Fields Medal award ceremony in 1954, Hermann Weyl gave high praise to Serre, and also made the point that the award was for the first time awarded to a non-analyst. Serre subsequently changed his research focus.
Algebraic geometry
[edit]In the 1950s and 1960s, a fruitful collaboration between Serre and the two-years-younger Alexander Grothendieck led to important foundational work, much of it motivated by the Weil conjectures. Two major foundational papers by Serre were Faisceaux Algébriques Cohérents (FAC, 1955),[3] on coherent cohomology, and Géométrie Algébrique et Géométrie Analytique (GAGA, 1956).[4]
Even at an early stage in his work Serre had perceived a need to construct more general and refined cohomology theories to tackle the Weil conjectures. The problem was that the cohomology of a coherent sheaf over a finite field could not capture as much topology as singular cohomology with integer coefficients. Amongst Serre's early candidate theories of 1954–55 was one based on Witt vector coefficients.
Around 1958 Serre suggested that isotrivial principal bundles on algebraic varieties – those that become trivial after pullback by a finite étale map – are important. This acted as one important source of inspiration for Grothendieck to develop the étale topology and the corresponding theory of étale cohomology.[5] These tools, developed in full by Grothendieck and collaborators in Séminaire de géométrie algébrique (SGA) 4 and SGA 5, provided the tools for the eventual proof of the Weil conjectures by Pierre Deligne.
Other work
[edit]From 1959 onward Serre's interests turned towards group theory, number theory, in particular Galois representations and modular forms.
Amongst his most original contributions were: his "Conjecture II" (still open) on Galois cohomology; his use of group actions on trees (with Hyman Bass); the Borel–Serre compactification; results on the number of points of curves over finite fields; Galois representations in ℓ-adic cohomology and the proof that these representations have often a "large" image; the concept of p-adic modular form; and the Serre conjecture (now a theorem) on mod-p representations that made Fermat's Last Theorem a connected part of mainstream arithmetic geometry.
In his paper FAC,[3] Serre asked whether a finitely generated projective module over a polynomial ring is free. This question led to a great deal of activity in commutative algebra, and was finally answered in the affirmative by Daniel Quillen and Andrei Suslin independently in 1976. This result is now known as the Quillen–Suslin theorem.
Honors and awards
[edit]Serre, at twenty-seven in 1954, was and still is the youngest person ever to have been awarded the Fields Medal. He went on to win the Balzan Prize in 1985, the Steele Prize in 1995, the Wolf Prize in Mathematics in 2000, and was the first recipient of the Abel Prize in 2003. He has been awarded other prizes, such as the Gold Medal of the French National Scientific Research Centre (Centre National de la Recherche Scientifique, CNRS).
He is a foreign member of several scientific Academies (US, Norway, Sweden, Russia, the Royal Society, Royal Netherlands Academy of Arts and Sciences (1978),[6] American Academy of Arts and Sciences,[7] National Academy of Sciences,[8] the American Philosophical Society[9]) and has received many honorary degrees (from Cambridge, Oxford, Harvard, Oslo and others). In 2012 he became a fellow of the American Mathematical Society.[10]
Serre has been awarded the highest honors in France as Grand Cross of the Legion of Honour (Grand Croix de la Légion d'Honneur) and Grand Cross of the Legion of Merit (Grand Croix de l'Ordre National du Mérite).
See also
[edit]- Multiplicity (mathematics)
- Bourbaki group — Serre joined it in the late 1940s
Bibliography
[edit]- Groupes Algébriques et Corps de Classes (1959), Hermann ISBN 9782705612641, translated into English as
- Algebraic Groups and Class Fields. Graduate Texts in Mathematics. Vol. 117. 1988. doi:10.1007/978-1-4612-1035-1. ISBN 978-1-4612-6993-9.
- Corps Locaux (1962), Hermann ISBN 9782705612962, as
- Local Fields. Graduate Texts in Mathematics. Vol. 67. 1979. doi:10.1007/978-1-4757-5673-9. ISBN 978-1-4757-5675-3.
- Cohomologie Galoisienne (1964) Collège de France course 1962–63, as
- Galois Cohomology. Springer Monographs in Mathematics. 1997. doi:10.1007/978-3-642-59141-9. ISBN 978-3-540-42192-4.
- Algèbre Locale, Multiplicités (1965) Collège de France course 1957–58, as
- Local Algebra. Springer Monographs in Mathematics. 2000. doi:10.1007/978-3-662-04203-8. ISBN 978-3-642-08590-1.
- Lie Algebras and Lie Groups. Lecture Notes in Mathematics. Vol. 1500. 1992. doi:10.1007/978-3-540-70634-2. ISBN 978-3-540-55008-2.
- Algèbres de Lie Semi-simples Complexes (1966), as
- Serre, Jean-Pierre (1987). Complex Semisimple Lie Algebras. doi:10.1007/978-1-4757-3910-7. ISBN 978-0-387-96569-7.
- Abelian ℓ-Adic Representations and Elliptic Curves (1968), reissue, Serre, Jean-Pierre (1997). Abelian ℓ-Adic Representations and Elliptic Curves. doi:10.1201/9781439863862. ISBN 9780429063015.[11]
- Cours d'arithmétique (1970), PUF, as
- A Course in Arithmetic. Graduate Texts in Mathematics. Vol. 7. 1973. doi:10.1007/978-1-4684-9884-4. ISBN 978-0-387-90041-4.
- Représentations linéaires des groupes finis (1971), Hermann, as
- Linear Representations of Finite Groups. Graduate Texts in Mathematics. Vol. 42. 1977. doi:10.1007/978-1-4684-9458-7. ISBN 978-1-4684-9460-0.[12]
- Arbres, amalgames, SL2 (1977), SMF, as
- Serre, Jean-Pierre (1980). Trees. doi:10.1007/978-3-642-61856-7. ISBN 978-3-642-61858-1.[13]
- Oeuvres/Collected Papers in four volumes (1986) Vol. IV in 2000, Springer-Verlag
- Serre, Jean-Pierre (2 December 2013). Oeuvres - Collected Papers I: 1949 - 1959. Springer. ISBN 978-3-642-39815-5.
- Serre, Jean-Pierre (4 December 2013). Oeuvres - Collected Papers II: 1960 - 1971. Springer. ISBN 978-3-642-37725-9.
- Serre, Jean-Pierre (14 April 2014). Oeuvres - Collected Papers III: 1972 - 1984. Springer. ISBN 978-3-642-39837-7.
- Serre, Jean-Pierre (19 December 2013). Oeuvres - Collected Papers IV: 1985 - 1998. Springer. ISBN 978-3-642-39839-1.
- Lectures on the Mordell-Weil Theorem. Aspects of Mathematics. Vol. 15. 1997. doi:10.1007/978-3-663-10632-6. ISBN 978-3-663-10634-0.
- Serre, Jean-Pierre (2016). Topics in Galois Theory. doi:10.1201/b10588. ISBN 9780429064401.[14]
- Exposés de séminaires 1950–1999 (2001), SMF, ISBN 9782856291030,ISBN 9782856292426
- Garibaldi, Skip; Merkurjev, Alexander; Serre, Jean-Pierre (2003). Cohomological Invariants in Galois Cohomology. American Mathematical Society. ISBN 978-1-4704-2174-8.
- Grothendieck, Alexandre; Colmez, Pierre (2004). Grothendieck-Serre Correspondence. American Mathematical Soc. ISBN 978-0-8218-3424-4.
- Serre, Jean-Pierre (2016). Lectures on N_X(p). doi:10.1201/b11315. ISBN 9780429067617.
- Correspondance Serre-Tate (2015), edited with Pierre Colmez, SMF, ISBN 9782856298022
- Finite Groups: an Introduction (2016), Higher Education Press & International Press, ISBN 9781571463272
- Rational Points on Curves over Finite Fields (2020), with contributions by E. Howe, J. Oesterlé, C. Ritzenthaler, SMF, ISBN 9782856299234
A list of corrections, and updating, of these books can be found on his home page at Collège de France.
Notes
[edit]- ^ J J O'Connor and E F Robertson Serre Biography http://www-history.mcs.st-andrews.ac.uk/Biographies/Serre.html
- ^ Serre, J. -P. (2009). "Henri Paul Cartan. 8 July 1904 -- 13 August 2008". Biographical Memoirs of Fellows of the Royal Society. 55: 37–44. doi:10.1098/rsbm.2009.0005.
- ^ a b Serre, Jean-Pierre (1955). "Faisceaux Algébriques Cohérents". The Annals of Mathematics. 61 (2): 197–278. doi:10.2307/1969915. JSTOR 1969915.
- ^ Serre, Jean-Pierre (1956), "Géométrie algébrique et géométrie analytique", Annales de l'Institut Fourier, 6: 1–42, doi:10.5802/aif.59, ISSN 0373-0956, MR 0082175
- ^ (in French) http://www.math.u-psud.fr/~illusie/Grothendieck_etale.pdf
- ^ "J.-P. Serre". Royal Netherlands Academy of Arts and Sciences. Archived from the original on 5 March 2016. Retrieved 4 August 2015.
- ^ "Jean-Pierre Serre". American Academy of Arts & Sciences. Retrieved 2 December 2021.
- ^ "Jean-Pierre Serre". www.nasonline.org. Retrieved 2 December 2021.
- ^ "APS Member History". search.amphilsoc.org. Retrieved 2 December 2021.
- ^ List of Fellows of the American Mathematical Society, retrieved 2013-07-18.
- ^ Ribet, Kenneth A. (1990). "Review: Abelian ℓ-adic representations and elliptic curves, by Jean-Pierre Serre" (PDF). Bull. Amer. Math. Soc. (N.S.). 22 (1): 214–218. doi:10.1090/s0273-0979-1990-15882-3.
- ^ Gustafson, W. H. (1978). "Review: Linear representations of finite groups, by Jean-Pierre Serre" (PDF). Bull. Amer. Math. Soc. 84 (5): 939–943. doi:10.1090/s0002-9904-1978-14540-6.
- ^ Alperin, Roger C. (1983). "Review: Group, trees and projective modules, by Warren Dicks; and Trees, by Jean-Pierre Serre" (PDF). Bull. Amer. Math. Soc. (N.S.). 8 (2): 401–405. doi:10.1090/s0273-0979-1983-15146-7.
- ^ Fried, Michael (1994). "Review: Topics in Galois Theory, by J.-P. Serre" (PDF). Bull. Amer. Math. Soc. (N.S.). 30 (1): 124–135. doi:10.1090/S0273-0979-1994-00445-8.
External links
[edit]- O'Connor, John J.; Robertson, Edmund F., "Jean-Pierre Serre", MacTutor History of Mathematics Archive, University of St Andrews
- Jean-Pierre Serre at the Mathematics Genealogy Project
- Jean-Pierre Serre, Collège de France, biography and publications.
- Jean-Pierre Serre Archived 11 June 2007 at the Wayback Machine at the French Academy of Sciences, in French.
- Interview with Jean-Pierre Serre in Notices of the American Mathematical Society.
- An Interview with Jean-Pierre Serre by C.T. Chong and Y.K. Leong, National University of Singapore.
- How to write mathematics badly a public lecture by Jean-Pierre Serre on writing mathematics.
- Biographical page Archived 11 June 2007 at the Wayback Machine (in French)
- 1926 births
- Living people
- People from Pyrénées-Orientales
- Foreign associates of the National Academy of Sciences
- 20th-century French mathematicians
- Abel Prize laureates
- Algebraic geometers
- Algebraists
- École Normale Supérieure alumni
- Academic staff of the École Normale Supérieure
- Nicolas Bourbaki
- Fields Medalists
- Academic staff of the Collège de France
- Foreign members of the Royal Society
- French number theorists
- Topologists
- University of Paris alumni
- Grand Cross of the Legion of Honour
- Wolf Prize in Mathematics laureates
- Members of the French Academy of Sciences
- Members of the Norwegian Academy of Science and Letters
- Members of the Royal Netherlands Academy of Arts and Sciences
- Foreign members of the Russian Academy of Sciences
- Fellows of the American Mathematical Society
- Institute for Advanced Study visiting scholars
- Members of the American Philosophical Society
- Members of the Royal Swedish Academy of Sciences
- Research directors of the French National Centre for Scientific Research