Analyse p-adique et représentations Galoisiennes

Details Analyse p-adique et représentations Galoisiennes Analyse p-adique et représentations Galoisiennes

2003-04-16

arxiv.org/abs/math/0304232v1

Proceedings of the ICM, Beijing 2002, vol. 2, 139--148

Mathematics

Number Theory

Scientific paper

The notion of a p-adic de Rham representation of the absolute Galois group of a p-adic field was introduced about twenty years ago (see e.g. [Fo93]). Three important results for this theory have been obtained recently: The structure theorem for the {\it almost $C_p$-representations}, the theorem {\it weakly admissible implies admissible} and the theorem {\it de Rham implies potentially semi-stable}. The proofs of the first two theorems are closely related to the study of a new kind of analytic groups, the {\it Banach-Colmez spaces} and the proof of the third uses deep results on p-{\it adic differential equations on the Robba ring}.

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