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Pierre Deligne

** Pierre René, Viscount Deligne ** (born 3 October 1944) is a [Belgian] [mathematician] . He is known for work on the [Weil conjectures] , leading finally to a complete proof in 1973.

** Life **

He was born in [Brussels] , and studied at the [Universite Libre de Bruxelles] (ULB).

After completing a [doctorate] under the supervision of [Alexander Grothendieck] , he worked with him at the [Institut des Hautes Études Scientifiques] (IHÉS) near [Paris] , initially on the generalization within [scheme theory] of [Zariski's main theorem] . In 1968, he also worked with [Jean-Pierre Serre] ; their work led to important results on the l-adic representations attached to [modular form] s, and the conjectural [functional equation] s of [L-function] s. Deligne's also focused on topics in [Hodge theory] . He introduced [weights] and tested them on objects in [complex geometry] . He also collaborated with [David Mumford] on a new description of the [moduli space] s for curves. Their work came be seen as an introduction to one form of the theory of [algebraic stack] s, and recently has been applied to questions arising from [string theory] . Perhaps Deligne's most famous contribution was his proof of the third and last of the [Weil conjectures] . This proof completed a programme initiated and largely developed by [Alexander Grothendieck] . As a corollary he proved the celebrated [Ramanujan-Petersson conjecture] for [modular forms] of weight greater than one; weight one was proved in his work with Serre. Deligne's paper (1974) contains the first proof of the [Weil conjectures] , Deligne's contribution being to supply the estimate of the eigenvalues of Frobenius, considered the geometric analogue of the [Riemann Hypothesis] .

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