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Pierre Deligne

Pierre Deligne
Deligne.jpg
Pierre Deligne, March 2005
Born (1944-10-03) 3 October 1944 (age 72)
Etterbeek, Belgium
Nationality Belgian
Fields Mathematics
Institutions Institute for Advanced Study
Institut des Hautes Études Scientifiques
Alma mater Université libre de Bruxelles
Doctoral advisor Alexander Grothendieck
Doctoral students Lê Dũng Tráng
Miles Reid
Michael Rapoport
Known for Proof of the Weil conjectures
Perverse sheaves
Notable awards Abel Prize (2013)
Wolf Prize (2008)
Balzan Prize (2004)
Crafoord Prize (1988)
Fields Medal (1978)

Pierre René, Viscount Deligne (French: [dəliɲ]; born 3 October 1944) is a Belgian mathematician. He is known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, and 1978 Fields Medal.

He was born in Etterbeek, attended school at Athénée Adolphe Max and studied at the Université 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 forms, and the conjectural functional equations of L-functions. 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 spaces for curves. Their work came to be seen as an introduction to one form of the theory of algebraic stacks, 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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