Analyse p-adique et Representations Galoisiennes

摘要

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 almost C_p-representations, the theorem weakly admissible implies admissible and the theorem 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 Banach-Colmez spaces and the proof of the third uses deep results on p-adic differential equations on the Robba ring.