p-adic Galois representations
Professor Jean-Marc Fontaine
Orsay University, Paris.
28-11-07 - : Lecture Series

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Abstract

Let $K$ be a $p$-adic field, $\overline K$ an algebraic closure of $K$ and $G_K={\rm Gal}(\overline K/K)$.

$p$-adic Hodge theory deals with the study of $p$-adic representations of $G_K$ coming from algebraic geometry. We will review some of the main tools of this theory:

-- classification of $G_K$-representations via \'{e}tale $(\varphi,\Gamma)$-modules,

-- computation of Galois cohomology,

-- de Rham, semi-stable and crystalline Galois representations,

-- Kedlaya's slope filtration theorem,

-- integral $p$-adic Hodge theory, with a special emphasis on Kisin's theory.

The precise content will be decided after the first talk.