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.
On the ramification of étale cohomology groups