Jean-Pierre Serre - Life and career, Early work, Foundational work in algebraic geometry and the Weil conjectures, Other work

Mathematician, born in Bages, S France. He studied at the Ecole Normale Supérieure, then worked at the Centre National de la Recherche Scientifique and the University of Nancy, becoming professor at the Collège de France in 1956. He has carried out research in homotopy theory, algebraic geometry, class field theory, group theory, and number theory. In 1954 he was awarded the Fields Medal, and in 2004 the Abel Prize.

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.

Life and career

Born in Bages, Serre was educated at the Lycée de Nîmes and then from 1945 to 1948 at the Ecole Normale Supérieure in Paris.

Early work

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.

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.

Foundational work in algebraic geometry and 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.

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.

Around 1958 Serre suggested that isotrivial covers of algebraic varieties — those that become trivial after pullback by a finite covering map — should be important.

In later years Serre was sometimes a source of counterexamples to over-optimistic extrapolations.

Other work

From 1959 onward Serre's interests turned towards number theory, in particular class field theory and the theory of complex multiplication.

Awards

Serre was awarded the Fields Medal (1954 - having just turned 28 at the time, he is the youngest winner to date), the Balzan Prize (1985), the Steele Prize (1995), and the Wolf Prize in Mathematics (2000).

Works

Groupes Algébriques et Corps de Classes (1959) as Algebraic Groups and Class Fields (1988) Corps Locaux (1962) as Local Fields (1980) Cohomologie Galoisienne (1964) Collège de France course 1962-3, as Galois Cohomology (1997) Algèbre Locale, Multiplicités (1965) Collège de France course 1957-8, as Local Algebra (2000) Lie Algebras and Lie Groups (1965) 1964 Harvard lectures Algèbres de Lie Semi-simples Complexes (1966) as Complex Semisimple Lie Algebras (1987) Abelian l-Adic Representations and Elliptic Curves (1968) Cours d'arithmétique (1970) as A Course in Arithmetic (1973) Représentations linéaires des groupes finis (1971) as Linear Representations of Finite Groups (1977) Arbres, amalgames, SL2(1977) as Trees (1980) Oeuvres/Collected Papers in four volumes (1986) Vol.