Curves and vector bundles in p-adic Hodge theory

摘要

This work is dedicated to the discovery, the definition, and the study of the fundamental curve in p-adic Hodge theory. For this we take the point of view to define and study the p-adic period rings as rings of holomorphic functions of the variable p. We then classify the vector bundles on the curve, a theorem that generalizes in some sense the classification theorem of vector bundles on the projective line. As an application we give geometric proofs of the two main theorems in p-adic Hodge theory : weakly admissible implies admissible, and de Rham implies potentially semi-stable.