Jean-Pierre Serre | |
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 Serre in 2003 | |
| Born | (1926-09-15)15 September 1926 (age 99) Bages,Pyrénées-Orientales, France |
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| Known for | (List of things named after Jean-Pierre Serre) |
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| Fields | Mathematics |
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| Thesis | Homologie singulière des espaces fibrés (1951) |
| Doctoral advisor | Henri Cartan |
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Jean-Pierre Serre (French:[sɛʁ]; born 15 September 1926) is a Frenchmathematician who has made contributions toalgebraic topology,algebraic geometry andalgebraic number theory. He was awarded theFields Medal in 1954 and the inauguralAbel Prize in 2003.
Born inBages,Pyrénées-Orientales, to pharmacist parents, Serre was educated at the Lycée de Nîmes. Then he studied at theÉcole Normale Supérieure inParis from 1945 to 1948.[1] He was awarded his doctorate from theSorbonne in 1951. From 1948 to 1954 he held positions at theCentre National de la Recherche Scientifique inParis. In 1956 he was elected professor at theCollège 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 writerClaudine Monteil. The French mathematicianDenis Serre is his nephew. He practices skiing, table tennis, and rock climbing (inFontainebleau).
From a very young age he was an outstanding figure in the school ofHenri Cartan,[2] working onalgebraic topology,several complex variables and thencommutative algebra andalgebraic geometry, where he introducedsheaf theory andhomological algebra techniques. Serre's thesis concerned theLeray–Serre spectral sequence associated to afibration. Together with Cartan, Serre established the technique of usingEilenberg–MacLane spaces for computinghomotopy 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.
In the 1950s and 1960s, a fruitful collaboration between Serre and the two-years-youngerAlexander Grothendieck led to important foundational work, much of it motivated by theWeil conjectures. Two major foundational papers by Serre wereFaisceaux Algébriques Cohérents (FAC, 1955),[3] oncoherent cohomology, andGéométrie 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 refinedcohomology theories to tackle the Weil conjectures. The problem was that the cohomology of acoherent sheaf over afinite field could not 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 finiteétale map – are important. This acted as one important source of inspiration for Grothendieck to develop theétale topology and the corresponding theory ofétale cohomology.[5] 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 byPierre Deligne.
From 1959 onward Serre's interests turned towardsgroup theory,number theory, in particularGalois representations andmodular forms.
Amongst his most original contributions were: his "Conjecture II" (still open) on Galois cohomology; his use ofgroup actions ontrees (withHyman Bass); the Borel–Serre compactification; results on the number of points of curves over finite fields;Galois representations inℓ-adic cohomology and the proof that these representations have often a "large" image; the concept ofp-adic modular form; and theSerre conjecture (now a theorem) on mod-p representations that madeFermat's Last Theorem a connected part of mainstreamarithmetic geometry.
In his paper FAC,[3] Serre asked whether a finitely generatedprojective module over apolynomial ring isfree. This question led to a great deal of activity incommutative algebra, and was finally answered in the affirmative byDaniel Quillen andAndrei Suslin independently in 1976. This result is now known as theQuillen–Suslin theorem.
Serre, at twenty-seven in 1954, was and still is the youngest person ever to have been awarded theFields Medal. He went on to win theBalzan Prize in 1985, theSteele Prize in 1995, theWolf Prize in Mathematics in 2000, and was the first recipient of theAbel 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] theAmerican Philosophical Society[9]) and has received many honorary degrees (from Cambridge, Oxford, Harvard, Oslo and others). In 2012 he became a fellow of theAmerican Mathematical Society.[10]
Serre has been awarded the highest honors in France asGrand Cross of the Legion of Honour (Grand Croix de la Légion d'Honneur) andGrand Cross of the Legion of Merit (Grand Croix de l'Ordre National du Mérite).
Alist of corrections, and updating, of these books can be found on his home page at Collège de France.
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