On a generalized Brauer group in mixed characteristic cases, II

Abstract

As an extension of an author's previous paper, we prove the Gersten-type conjecture for the mod $p$ étale 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.

52 pages, Theorem 1.3 in this version is an extension of Theorem 1.1 in v.2, Theorem 1.6 in this version is an extension of Theorem 1.2 in v.2