A Bloch–Ogus theorem for henselian local rings in mixed characteristic

Abstract

We show a conditional exactness statement for the Nisnevich Gersten complex associated to an A1-invariant cohomology theory with Nisnevich descent for smooth schemes over a Dedekind ring with only infinite residue fields. As an application we derive a Nisnevich analogue of the Bloch–Ogus theorem for étale cohomology over a henselian discrete valuation ring with infinite residue field.