Seminars

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