Non-torsion Brauer groups in positive characteristic

TL;DR

This paper investigates the properties of Brauer groups in positive characteristic, revealing that certain algebraic surfaces can have non-torsion Brauer groups, unlike over finite fields.

Contribution

It demonstrates the existence of integral normal projective surfaces with non-torsion Brauer groups in positive characteristic, contrasting with the torsion property over algebraic closures of finite fields.

Findings

Existence of non-torsion Brauer groups on certain surfaces in positive characteristic

Non-existence of such examples over algebraic closures of finite fields

Highlights differences between Brauer groups in various algebraic settings

Abstract

Unlike the classical Brauer group of a field, the Brauer-Grothendieck group of a singular scheme need not be torsion. We show that there exist integral normal projective surfaces over a large field of positive characteristic with non-torsion Brauer group. In contrast, we demonstrate that such examples cannot exist over the algebraic closure of a finite field.