Jean-Marc Fontaine passed away in January 2019. He is famous for his rings and his program of classification of representations of the absolute Galois groups of local fields that turned -adic Hodge theory into one of the most powerful tool of arithmetic geometry and algebraic number theory. We give an overview of this program with an emphasis on Fontaine’s own contributions to it.
Cite this article
Pierre Colmez, Le programme de Fontaine. Enseign. Math. 65 (2019), no. 3/4, pp. 487–531DOI 10.4171/LEM/65-3/4-7