# A Bloch-Ogus Theorem for henselian local rings in mixed characteristic

## TL;DR

This paper establishes a Nisnevich analogue of the Bloch-Ogus theorem for étale cohomology over henselian discrete valuation rings with infinite residue fields, extending the understanding of cohomological complexes in mixed characteristic.

## Contribution

It proves a conditional exactness for the Nisnevich Gersten complex for A^1-invariant cohomology theories over Dedekind rings, leading to a new Bloch-Ogus type result in mixed characteristic.

## Key findings

- Conditional exactness of the Nisnevich Gersten complex
- Nisnevich analogue of the Bloch-Ogus theorem for étale cohomology
- Extension of cohomological tools to mixed characteristic settings

## 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.