Brauer group of varieties over local fields of finite characteristic

Abstract

We show that the nonlogarithmic version of Kato's ramification filtration on the Brauer group of a separated regular scheme of finite type over a henselian discrete valuation field of positive characteristc with finite residue field coincides with the evaluation filtration. This extends a recent result of Bright and Newton to positive characteristic. As applications, we extend several results of Ieronymou, Saito and Sato, and Kai to positive characteristic.

Minor corrections, 98 pages