- Jean-Pierre Serre
Infobox Scientist

name = Jean-Pierre Serre

birth_date = birth date and age|1926|09|15

birth_place = Bages,Pyrénées-Orientales ,France

residence =Paris ,France

nationality =France

field =Mathematics

work_institutions =Centre National de la Recherche Scientifique Collège de France

alma_mater =École Normale Supérieure

doctoral_advisor =

doctoral_students =

known_for =

author_abbrev_bot =

author_abbrev_zoo =

influences =

influenced =

prizes =Abel Prize (2003)Fields Medal (1954)Wolf Prize in Mathematics (2000)

footnotes =**Jean-Pierre Serre**(bornSeptember 15 ,1926 ) is one of the leadingmathematician s of the twentieth century, active inalgebraic geometry ,number theory andtopology . He has received numerous awards and honors for his mathematical research and exposition, including theFields Medal in 1954 and theAbel Prize in 2003.**Biography**Born in Bages,

Pyrénées-Orientales ,France , Serre was educated at theLycée de Nîmes and then from 1945 to 1948 at theÉcole Normale Supérieure inParis . He was awarded his doctorate from the Sorbonne in 1951. From 1948 to 1954 he held positions at theCentre National de la Recherche Scientifique inParis . He is currently a professor at theCollège de France .**Career**From a very young age he was an outstanding figure in the school of

Henri Cartan , working onalgebraic topology ,several complex variables and thencommutative algebra andalgebraic geometry , in the context of sheaf theory andhomological algebra techniques. Serre's thesis concerned the Leray–Serre spectral sequence associated to afibration . Together with Cartan, Serre established the technique of usingEilenberg-MacLane space s for computinghomotopy groups of spheres , which at that time was considered as the major problem in topology.In his speech at the Fields Medal award ceremony in 1954,

Hermann Weyl praised Serre in seemingly extravagant terms, and also made the point that the award was for the first time awarded to an algebraist. Serre subsequently changed his research focus; he apparently thought thathomotopy theory , where he had started, was already overly technical. However, Weyl's perception that the central place of classical analysis had been challenged byabstract algebra has subsequently been justified, as has his assessment of Serre's place in this change.**Work on algebraic geometry**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 theWeil conjectures . Two major foundational papers by Serre were "Faisceaux Algébriques Cohérents" (FAC), oncoherent cohomology ) and "Géometrie Algébrique et Géométrie Analytique" (GAGA ).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 acoherent sheaf over afinite field couldn't capture as much topology assingular cohomology with integer coefficients. Amongst Serre's early candidate theories of 1954–55 was one based onWitt 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 developétale topology and the corresponding theory ofétale cohomology . These tools, developed in full by Grothendieck and collaborators inSéminaire de géométrie algébrique (SGA) 4 and SGA 5, provided the tools for the eventual proof of the Weil conjectures.In later years Serre was sometimes a source of counterexamples to over-optimistic extrapolations. He also had a close working relationship with

Pierre Deligne , who eventually finished the proof of the Weil conjectures.**Other work**From 1959 onward Serre's interests turned towards

number theory , in particularclass field theory and the theory ofcomplex multiplication .Amongst his most original contributions were: the concept of

algebraic K-theory ; theGalois representation theory for ℓ-adic cohomology and the conceptions that these representations were "large"; and the Serre conjecture on mod-"p" representations that madeFermat's last theorem a connected part of mainstreamarithmetic geometry .**Honours and awards**Serre, at twenty-seven in 1954, is the youngest ever to be awarded the

Fields Medal . In 1985, he went on to win theBalzan Prize , theSteele Prize in 1995, theWolf Prize in Mathematics in 2000, and is the first recipient of theAbel Prize in 2003. Serre and John Thompson are the only laureates of all three of the Fields Medal, the Wolf Prize, and the Abel Prize.**ee also***

Serre duality

*Serre's multiplicity conjectures

*Serre's property FA

*Serre conjecture (number theory)

*Serre spectral sequence

*Serre fibration

*Serre twist sheaf

*Thin set in the sense of Serre

*Quillen-Suslin theorem

*Nicolas Bourbaki **Bibliography***"Groupes Algébriques et Corps de Classes" (1959) as "Algebraic Groups and Class Fields" (1988)

*"Corps Locaux" (1962) as "Local Fields" (1980)

*"Cohomologie Galoisienne" (1964) Collège de France course 1962–3, as "Galois Cohomology" (1997)

*"Algèbre Locale, Multiplicités" (1965) Collège de France course 1957–8, as "Local Algebra" (2000)

*"Lie Algebras and Lie Groups" (1965) 1964 Harvard lectures

*"Algèbres de Lie Semi-simples Complexes" (1966) as "Complex Semisimple Lie Algebras" (1987)

*"Abelian ℓ-Adic Representations and Elliptic Curves" (1968)

*"Cours d'arithmétique" (1970) as "A Course in Arithmetic " (1973)

*"Représentations linéaires des groupes finis" (1971) as "Linear Representations of Finite Groups" (1977)

*"Arbres, amalgames, SL_{2}"(1977) as "Trees" (1980)

*"Oeuvres/Collected Papers in four volumes" (1986) Vol. IV in 2000

*"Lectures on the Mordell-Weil Theorem" (1990)

*"Topics in Galois Theory" (1992)

*"Motives" (1994) two volumes, editor with Uwe Jannsen and Steven L. Kleiman

*"Cohomological Invariants in Galois Cohomology" (2003) with Skip Garibaldi and Alexander Merkurjev

* Citation

last = Serre

first = Jean-Pierre

author-link =

title = Exposés de séminaires 1950–1999

publisher = Société Mathématique de France

year = 2001

isbn = 2-85629-103-1

*"Grothendieck–Serre Correspondence" (2003) edited with Pierre Colmez**External links***

*

* [*http://www.academie-sciences.fr/membres/S/Serre_JP.htm Jean-Pierre Serre*] at theFrench Academy of Sciences , in French.

* [*http://www.college-de-france.fr/default/EN/all/ins_pro/essai.htm Jean-Pierre Serre*] at theCollège de France , in French.Persondata

NAME= Serre, Jean-Pierre

ALTERNATIVE NAMES=

SHORT DESCRIPTION=French mathematician and Fields medallist.

DATE OF BIRTH=September 15 ,1926

PLACE OF BIRTH= Bages,Pyrénées-Orientales ,France

DATE OF DEATH=

PLACE OF DEATH=

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