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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 Collège de FranceThe College de France is a higher education teaching and research establishment located in Paris, France. It was created in 1530 at the request of King Francis I of France. Of humanist inspiration, this school was established as an alternative to the Sorb.
From very young he was an outstanding figure in the school of Henri CartanHenri Cartan (born July 8, 1904) is a son of Elie Cartan, and is, as his father was, a distinguished and influential mathematician. Born in in Nancy, France. He studied at the Lycee Hoche in Versailles, then at the ENS. He held academic positions at a num, working on algebraic topologyTopology Algebraic topology Abstract algebra Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. The method of algebraic invariants The goal is to take topological spaces, and further ca, several complex variablesThe theory of functions of several complex variables is the branch of mathematics dealing with functions f ''z, z,. z on the space C n of n tuples of complex numbers. As in complex analysis, which is the case n 1 but of a distinct character, these are not and then commutative algebraIn abstract algebra, commutative algebra is the field of study of commutative rings, their ideals, modules and algebras. It is foundational both for algebraic geometry and for algebraic number theory. The most prominent example for commutative rings are p and algebraic geometry; in a context of sheafAlternate meanings: River Sheaf, King Sceaf, sheaf toss In mathematics, a sheaf ''F on a given topological space X gives a set or richer structure F ''U for each open set U of X''. The structures F ''U are compatible with the operations of restricting the 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 Serre'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 .
Serre was awarded the Fields Medal in 1954, and was the first recipient of the Abel Prize in 2003. He also received the Balzan Prize (1985), the Steele Prize (1995), and the Wolf Prize (2000).