Théorie de Sen et vecteurs localement analytiques

Abstract

We generalize Sen theory to extensions $K_{\infty }/K$ whose Galois group is a $p$-adic Lie group of arbitrary dimension. To do so, we replace Sen's space of $K$-finite vectors by Schneider and Teitelbaum's space of locally analytic vectors. One then gets a vector space over the field of locally analytic vectors of ${\hat{K}}_{\infty }$. We describe this field in general and pay a special attention to the case of Lubin-Tate extensions.

29 pages, in French