Personal life 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. 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 From a very young age, Serre was an outstanding figure in the school of
Henri Cartan, 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 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), on
coherent cohomology, and
Géométrie Algébrique et Géométrie Analytique (
GAGA, 1956). 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. 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
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, 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==