Purity for Hodge-Tate representations

Abstract

We prove that a kind of purity holds for Hodge-Tate representations of the fundamental group of the generic fiber of a semi-stable scheme over a complete discrete valuation ring of mixed characteristic with perfect residue field. As an application, we see that the relative p-adic etale cohomology with proper support of a scheme separated of finite type over the generic fiber is Hodge-Tate if it is locally constant.