On Problems about a generalization of the Brauer group

Makoto Sakagaito

Published 2015-11-30Version 1

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 an excellent two dimensional regular local ring which is smooth over a spectrum of a discrete valuation ring of characteristic $p>0$. Moreover we consider a generalization of Artin's theorem on Brauer groups.