On Problems about a generalization of the Brauer group

Abstract

In this paper, we define a generalization of the Brauer groups by using Bloch's cycle complex on etale site. We prove the Gersten conjecture of generalized Brauer group on some cases. As an application we prove the Gersten conjecture of the logarithmic Hodge-Witt cohomology for a two dimensional regular local ring which is smooth over a spectrum of some discrete valuation ring of characteristic $p>0$. Moreover we consider a generalization of Artin's theorem on Brauer groups.

arXiv comment26 pages, added Lemma 4.1, Proposition 4.1, Remark 2,3 and section 5, revised Remark 6, Theorem 4.1 and argument in section 6

Cited by in corpus (2)

• A note on Gersten's conjecture for étale cohomology over two-dimensional henselian regular local rings
• On a generalized Brauer group in mixed characteristic cases