Universal triviality of the Chow group of 0-cycles and the Brauer group

TL;DR

This paper proves that for certain smooth, proper varieties over a field, the triviality of the Chow group of 0-cycles implies the triviality of the Brauer group, addressing a gap related to p-torsion in characteristic p.

Contribution

It establishes the universal triviality of the Brauer group for universally CH_0-trivial varieties, extending understanding in algebraic geometry and Brauer group theory.

Findings

Universal CH_0-triviality implies trivial Brauer group.

Addresses p-torsion issues in characteristic p.

Fills a gap in the literature on algebraic cycles and Brauer groups.

Abstract

We prove that a smooth proper universally CH_0-trivial variety X over a field k has universally trivial Brauer group. This fills a gap in the literature concerning the p-torsion of the Brauer group when k has characteristic p.