# Jean-Pierre Serre

**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. Serre was awarded the Fields Medal in 1954, and was the first recipient of the Abel Prize in 2003.

He was educated at the Lycée de Nimes and then from 1945 to 1948 at the Ecole Normale Supérieure in Paris. Serre 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 a member of the French Academy of Science.

From very young 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 a context of sheaf theory and homological algebra techniques. In his speech at the Fields Medal award ceremony in 1954, Hermann Weyl praised Serre in apparently extravagant terms; and also made the point that the award was for the first time awarded to an algebraist. While Serre subsequently moved field - at this point he apparently thought that homotopy theory where he had started was already over-technical - 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.

In the 1950s and 1960s, a fruitful collaboration between Serre and the two years younger Alexander Grothendieck lead to important foundational work, much of it motivated by the Weil conjectures. Serre had early on perceived a need to construct general cohomology theories to tackle these conjectures, and Grothendieck eventually delivered. Amongst Serr's candidate theories (1954/5) was one based on Witt vector coefficients. Around 1958 Serre suggested that isotrivial covers of algebraic varieties should be important - those that become trivial after pullback by a finite covering map. This was one important step towards the eventual *étale covering* theory. In the later developments Serre was sometimes a source instead of counterexamples. From 1959 onwards his 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.

See also: Serre duality