Everything about Jean-pierre Serre totally explained
Jean-Pierre Serre (born
September 15,
1926) is one of the leading
mathematicians of the
twentieth century, active in
algebraic geometry,
number theory and
topology. He has received numerous awards and honors for his mathematical research and exposition, including the
Fields Medal in 1954 and the
Abel Prize in 2003.
Biography
Born in
Bages,
Pyrénées-Orientales,
France, Serre was educated at the
Lycée de Nîmes and then from 1945 to 1948 at the
École Normale Supérieure in
Paris. 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. He is currently a professor at the
Collège de France.
Career
From a very young age he was an outstanding figure in the school of
Henri Cartan, working on
algebraic topology,
several complex variables and then
commutative algebra and
algebraic geometry, in the context of
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 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 that
homotopy theory, where he'd started, was already overly technical. However, Weyl's perception that the central place of classical analysis had been challenged by
abstract algebra has subsequently been justified, as has his assessment of Serre's place in this change.
The Weil conjectures
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), on
coherent 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 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. 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.
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 particular
class field theory and the theory of
complex multiplication.
Amongst his most original contributions were: the concept of
algebraic K-theory; the
Galois representation theory for
ℓ-adic cohomology and the conceptions that these representations were "large"; and the
Serre conjecture on mod-
p representations that made
Fermat's last theorem a connected part of mainstream
arithmetic 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 the
Balzan Prize, the
Steele Prize in 1995, the
Wolf Prize in Mathematics in 2000, and is the first recipient of the
Abel 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.
Further Information
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