On the ramification of étale cohomology groups

Abstract

Let $K$ be a complete discrete valuation field whose residue field is perfect and of positive characteristic, let $X$ be a connected, proper scheme over ${\mathcal{O}}_K$, and let $U$ be the complement in $X$ of a divisor with simple normal crossings. Assume that the pair $(X,U)$ is strictly semi-stable over ${\mathcal{O}}_K$ of relative dimension one and $K$ is of equal characteristic. We prove that, for any smooth $\ell$-adic sheaf $\mathcal{G}$ on $U$ of rank one, at most tamely ramified on the generic fiber, if the ramification of $\mathcal{G}$ is bounded by $t+$ for the logarithmic upper ramification groups of Abbes-Saito at points of codimension one of $X$, then the ramification of the étale cohomology groups with compact support of $\mathcal{G}$ is bounded by $t+$ in the same sense.

References in corpus (1)

• Ramification theory for varieties over a local field

Cited by in corpus (1)

• Semi-continuity of conductors, and ramification bound of nearby cycles