Topos co-évanescents et généralisations

Abstract

This article is devoted to studying a topos introduced by Faltings for the purpose of $p$-adic Hodge theory. We present a new approach based on a generalisation of Deligne's co-vanishing topos. Along the way, we correct Faltings' original definition.

in French; an English version will appear in the volume 193 of Annals of Mathematics Studies (PUP) edited by A. Abbes, M. Gros and T. Tsuji; an unnecessary condition has been removed from corollary 10.27 and some minor modifications have been made accordingly