Splitting unramified Brauer classes by abelian torsors and the period-index problem

Abstract

We use twisted relative Picard varieties to split Brauer classes on projective varieties over algebraically closed fields by torsors for a fixed abelian scheme independent of the Brauer class. The construction is also used to prove that the index of an unramified Brauer class divides a fixed power of its period.

19 pages. Introduction rewritten, references added, results unchanged