On a generalized Brauer group in mixed characteristic cases, II

TL;DR

This paper extends previous work by proving the Gersten-type conjecture for mod p étale motivic cohomology over local rings of mixed characteristic and establishes -homotopy invariance for a generalized Brauer group.

Contribution

It proves the Gersten-type conjecture in mixed characteristic and demonstrates -homotopy invariance for the generalized Brauer group, generalizing Saltman's results.

Findings

Proved Gersten-type conjecture for mod p étale motivic cohomology.

Established -homotopy invariance for the generalized Brauer group.

Extended results to mixed characteristic cases.

Abstract

As an extension of an author's previous paper, we prove the Gersten-type conjecture for the mod $p$ \'{e}tale motivic cohomology over a local ring of mixed characteristic $(0, p)$. We also prove the $\mathbb{P}^{1}$-homotopy invariance for the generalized Brauer group which is a genelization of a result due to Saltman in mixed characteristic cases.