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 $\mathbb{A}^1$-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 \'etale cohomology over a henselian discrete valuation ring with infinite residue field.