Jean-Marc Fontaine

Jean -Marc Fontaine ( born March 13, 1944 in Boulogne- Billancourt ) is a French mathematician who deals with algebraic geometry and number theory.

Fontaine studied at the École polytechnique in 1962, was from 1965 to 1971 scientist at CNRS and received his doctorate in 1972. 1971/72 he was at the University of Paris VI and from 1972 to 1988 at the University of Grenoble ( only Maître de conférences, then Professor ). Since 1989 he is professor at the University of Paris-Sud XI, Orsay.

Fontaine classified in one of his first works, the - divisible groups on the ring of integers of a local field and designed the body of the -adic periods, the -adic analogue of the case of complex numbers. He led a hierarchy - adic representations of the absolute Galois group of a -adic body a ( crystalline, semi- stable and de Rham representations ). In this area, a significant number of techniques and assumptions of it. He is a co-founder of the p-adic Hodge theory and its application in number theory. He proved that there is no non-trivial abelian varieties over the rational numbers with everywhere good reduction ( Il n'y a pas de variété abélienne sur Z, Inventiones Mathematicae Bd.81, 1985, S.515 ). He originated the concept of geometric Galoisdarstellung the Galois group of a number field ( and a guess with Barry Mazur, when global p -adic Galois representations geometric origin have ). He also worked on the Bloch- Kato conjecture.

In 1984 he received the Prix Carrière of the French Academy of Sciences. Since 2002 he is member of the French Academy of Sciences. In 2002 he received the Gay - Lussac- Humboldt Prize. He was invited speaker at the International Mathematical Congresses in Warsaw 1983 ( Representations of p- adique ) and Beijing 2002 ( analysis p- adique et represenatations galoisiennes ).

Among his doctoral Christophe Breuil (1996 ), Pierre and Jean -Pierre Colmez Wintenberger.

Writings

• Groupes p- divisibles sur les corps locaux. Astérisque, Bd.47/48, Societe Mathematique de France, 1977.
• Publisher: PERIODES - adiques. Astérisque, Bd.223, 1994.
• Published by Pierre Berthelot, Luc Illusie, Kazuya Kato, Michael Rapoport: Cohomologies - adiques et applications Arithmétiques. Astérisque Bd.278/279, 2002.