JeanPierre Serre
JeanPierre Serre  

JeanPierre Serre at Oberwolfach in 2009


Born 
Bages, PyrénéesOrientales, France 
15 September 1926
Residence  Paris, France 
Nationality  French 
Alma mater  
Awards 

Scientific career  
Fields  Mathematics 
Institutions  
Doctoral advisor  Henri Cartan 
Doctoral students 
JeanPierre 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 and the Abel Prize in 2003.
Contents
Biography
Personal life
Born in Bages, PyrénéesOrientales, France, to pharmacist parents, Serre was educated at the Lycée de Nîmes and then from 1945 to 1948 at the École Normale Supérieure in Paris.^{[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 HeulotSerre, 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
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 nonanalyst. Serre subsequently changed his research focus. However, Weyl's perception that the central place of classical analysis had been challenged has subsequently been justified, as has his assessment of Serre's place in this change.
Algebraic geometry
In the 1950s and 1960s, a fruitful collaboration between Serre and the twoyearsyounger 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),^{[3]} on coherent cohomology, and Géometrie Algébrique et Géométrie Analytique (GAGA).^{[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 couldn't 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 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
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 ℓadic cohomology and the proof that these representations have often a "large" image; the concept of padic modular form; and the Serre conjecture (now a theorem) on modp representations that made Fermat's last theorem a connected part of mainstream arithmetic geometry.
In his paper FAC, 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
Serre, at twentyseven in 1954, is the youngest ever to be 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 (France, US, Norway, Sweden, Russia, the Royal Society, Royal Netherlands Academy of Arts and Sciences (1978)^{[6]}) and has received many honorary degrees (from Cambridge, Oxford, Harvard, and others). In 2012 he became a fellow of the American Mathematical Society.^{[7]}
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
Bibliography
 Groupes Algébriques et Corps de Classes (1959), Hermann, translated into English as Algebraic Groups and Class Fields (1988), SpringerVerlag
 Corps Locaux (1962), Hermann, as Local Fields (1980), SpringerVerlag
 Cohomologie Galoisienne (1964) Collège de France course 1962–63, as Galois Cohomology (1997), SpringerVerlag
 Algèbre Locale, Multiplicités (1965) Collège de France course 1957–58, as Local Algebra (2000), SpringerVerlag
 "Lie algebras and Lie groups" (1965) Harvard Lectures, SpringerVerlag.
 Algèbres de Lie Semisimples Complexes (1966), as Complex Semisimple Lie Algebras (1987), SpringerVerlag
 Abelian ℓAdic Representations and Elliptic Curves (1968), CRC Press, reissue. AddisonWesley. 1989.^{[8]}
 Cours d'arithmétique (1970), PUF, as A Course in Arithmetic (1973), SpringerVerlag
 Représentations linéaires des groupes finis (1971), Hermann, as Linear Representations of Finite Groups (1977), SpringerVerlag^{[9]}
 Arbres, amalgames, SL_{2} (1977), SMF, as Trees (1980), SpringerVerlag^{[10]}
 Oeuvres/Collected Papers in four volumes (1986) Vol. IV in 2000, SpringerVerlag
 Lectures on the MordellWeil Theorem (1990), Vieweg
 Topics in Galois Theory (1992), CRC Press^{[11]}
 "Cohomological Invariants in Galois Cohomology (2003) with Skip Garibaldi and Alexander Merkurjev, AMS
 "Exposés de séminaires 1950–1999" (2001), SMF
 Grothendieck–Serre Correspondence (2003), bilingual edition, edited with Pierre Colmez, SMFAMS
 "Lectures on N_X(p)" (2012), AK Peters, CRC Press
 Correspondance SerreTate (2015), edited with Pierre Colmez, SMF
 "Finite Groups: an Introduction" (2016), Higher Education Press & International Press
Notes
 ^ J J O'Connor and E F Robertson Serre Biography http://wwwhistory.mcs.standrews.ac.uk/Biographies/Serre.html
 ^ Serre, J. P. (2009). "Henri Paul Cartan". Biographical Memoirs of Fellows of the Royal Society. 55: 37–44. doi:10.1098/rsbm.2009.0005.
 ^ Serre, JeanPierre (1955). "Faisceaux Algebriques Coherents". The Annals of Mathematics. 61 (2): 197–278. doi:10.2307/1969915.
 ^ Serre, JeanPierre (1956), "Géométrie algébrique et géométrie analytique", Université de Grenoble. Annales de l'Institut Fourier, 6: 1–42, doi:10.5802/aif.59, ISSN 03730956, MR 0082175
 ^ (in French) http://www.math.upsud.fr/~illusie/Grothendieck_etale.pdf
 ^ "J.P. Serre". Royal Netherlands Academy of Arts and Sciences. Retrieved 4 August 2015.
 ^ List of Fellows of the American Mathematical Society, retrieved 20130718.
 ^ Ribet, Kenneth A. (1990). "Review: Abelian ℓadic representations and elliptic curves, by JeanPierre Serre" (PDF). Bull. Amer. Math. Soc. (N.S.). 22 (1): 214–218. doi:10.1090/s027309791990158823.
 ^ Gustafson, W. H. (1978). "Review: Linear representations of finite groups, by JeanPierre Serre" (PDF). Bull. Amer. Math. Soc. 84 (5): 939–943. doi:10.1090/s000299041978145406.
 ^ Alperin, Roger C. (1983). "Review: Group, trees and projective modules, by Warren Dicks; and Trees, by JeanPierre Serre" (PDF). Bull. Amer. Math. Soc. (N.S.). 8 (2): 401–405. doi:10.1090/s027309791983151467.
 ^ 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/S027309791994004458.
External links
 O'Connor, John J.; Robertson, Edmund F., "JeanPierre Serre", MacTutor History of Mathematics archive, University of St Andrews.
 JeanPierre Serre, Collège de France, biography and publications.
 JeanPierre Serre at the French Academy of Sciences, in French.
 Interview with JeanPierre Serre in Notices of the American Mathematical Society.
 An Interview with JeanPierre Serre by C.T. Chong and Y.K. Leong, National University of Singapore.
 How to write mathematics badly a public lecture by JeanPierre Serre on writing mathematics.
 Biographical page (in French)
 1926 births
 Living people
 People from PyrénéesOrientales
 Members of the United States National Academy of Sciences
 20thcentury mathematicians
 Abel Prize laureates
 Algebraic geometers
 Algebraists
 École Normale Supérieure alumni
 École Normale Supérieure faculty
 Nicolas Bourbaki
 Fields Medalists
 Collège de France faculty
 Foreign Members of the Royal Society
 French mathematicians
 Number theorists
 Topologists
 University of Paris alumni
 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