Non-torsion Brauer groups in positive characteristic

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.

arXiv comment5 pages. Comments welcome! v3: final version, to appear in Proceedings of the American Mathematical Society