Jean-Marc Fontaine (13 March 1944 – 29 January 2019) was a French mathematician. He was one of the founders of

p-adic Hodge theory In mathematics, ''p''-adic Hodge theory is a theory that provides a way to classify and study ''p''-adic Galois representations of characteristic 0 local fields with residual characteristic ''p'' (such as Q''p''). The theory has its beginnings in ...

. He was a professor at

Paris-Sud 11 University Paris-Sud University (French: ''Université Paris-Sud''), also known as University of Paris — XI (or as Université d'Orsay before 1971), was a French research university distributed among several campuses in the southern suburbs of Paris, in ...

from 1988 to his death.

Life

In 1962 Fontaine entered the

École Polytechnique École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

, from 1965 to 1971 was a researcher at CNRS and received his doctorate in 1972. From 1971 to 72 he was at the University of Paris VI and from 1972 to 1988 was at the University of Grenoble (only Maître de Conferences, but later a professor). From 1989 he was professor at the University of Paris-Sud XI in Orsay. Among his first works was the classification of ''p''-divisible groups (= Barsotti–Tate group) over the

ring of integers In mathematics, the ring of integers of an algebraic number field K is the ring of all algebraic integers contained in K. An algebraic integer is a root of a monic polynomial with integer coefficients: x^n+c_x^+\cdots+c_0. This ring is often deno ...

of a local field and the field of ''p''-adic periods, a ''p''-adic analogue of the field of complex numbers. Fontaine is one of the founders of

p

-adic Hodge theory. He proved that there are no non-trivial abelian varieties over the rational numbers with good reduction everywhere (''Il n'y a pas de variété abélienne sur Z'',

Inventiones Mathematicae ''Inventiones Mathematicae'' is a mathematical journal published monthly by Springer Science+Business Media. It was established in 1966 and is regarded as one of the most prestigious mathematics journals in the world. The current managing editors ...

vol. 81, 1985, p. 515). He introduced the concept of geometric Galois representation of the Galois group of a number field. He also worked on Bloch-Kato conjectures. In 1984 he received the Prix Carrière from the French Academy of Sciences. Beginning in 2002 he was a member of the

French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...

. In 2002 he was awarded the Gay-Lussac-Humboldt Prize. He was an invited speaker at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

in Warsaw 1983 (Représentations p-adiques) and Beijing 2002 (analyse p-adique et représentations galoisiennes). His students included

Christophe Breuil Christophe Breuil (; born 1968) is a French people, French mathematician, who works in arithmetic geometry and algebraic number theory. Work With Fred Diamond, Richard Taylor (mathematician), Richard Taylor and Brian Conrad in 1999, he proved th ...

Pierre Colmez Pierre Colmez (born 1962) is a French mathematician, notable for his work on ''p''-adic analysis. Colmez studied at École Normale Supérieure and obtained his doctorate from Grenoble University. He won the 2005 Fermat Prize for his contribution ...

, and Jean-Pierre Wintenberger.

Writings

* ''Groupes p-divisible sur les corps locaux''. Astérisque, Bd.47/48, Societe Mathematique de France, 1977. * ''periodes p-adiques.'' Astérisque, Bd.223, 1994. * With

Pierre Berthelot Pierre Berthelot (; born 1943) is a mathematician at the University of Rennes. He developed crystalline cohomology and rigid cohomology. Publications *Berthelot, Pierre ''Cohomologie cristalline des schémas de caractéristique p>0.'' Lecture ...

Luc Illusie Luc Illusie (; born 1940) is a French mathematician, specializing in algebraic geometry. His most important work concerns the theory of the cotangent complex and deformations, crystalline cohomology and the De Rham–Witt complex, and logarithmic ...

Kazuya Kato is a Japanese mathematician. He grew up in the prefecture of Wakayama in Japan. He attended college at the University of Tokyo, from which he also obtained his master's degree in 1975, and his PhD in 1980. He was a professor at Tokyo University ...

Michael Rapoport Michael Rapoport (born 2 October 1948) is an Austrian mathematician. Career Rapoport received his PhD from Paris-Sud 11 University in 1976, under the supervision of Pierre Deligne. He held a chair for arithmetic algebraic geometry at the Univ ...

: ''Cohomologies p-adiques et Arithmétiques applications. Astérisque Bd.278/279, 2002. * With

Barry Mazur Barry Charles Mazur (; born December 19, 1937) is an American mathematician and the Gerhard Gade University Professor at Harvard University. His contributions to mathematics include his contributions to Wiles's proof of Fermat's Last Theorem in ...

,
Geometric Galois representations
'

Prizes

* Cours Peccot du Collège de France (1973) * Prix Carrière de l'Académie des sciences (1984) * Prix Humboldt-Gay Lussac de la foundation Alexander von Humboldt (2002)

References

*https://web.archive.org/web/20081207113207/http://www.academie-sciences.fr/membres/F/Fontaine_JM_bio.htm *

External links

* {{DEFAULTSORT:Fontaine, Jean-Marc 1944 births 2019 deaths Members of the French Academy of Sciences 20th-century French mathematicians 21st-century French mathematicians

Life

Writings

Prizes

See also

References

External links