La conjecture $\epsilon$ locale de Kato en dimension $2$

Abstract

We show an Iwasawa functional equation for a two dimensional $p$-adic representation of the absolute Galois group of ${\mathbf{Q}}_p$. This allows us to complete Nakamura's proof of Kato's local $\epsilon$-conjecture in dimension $2$.

28 pages, submitted. In french. Several small modifications following the referees comments. Section 2.4 completely changed. To appear in Mathematische Annalen