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

## TL;DR

This paper explores how Brauer classes on projective varieties can be split using abelian torsors and relates the period and index of these classes.

## Contribution

The paper introduces a new method using twisted relative Picard varieties to split Brauer classes with torsors independent of the class.

## Key findings

- Twisted relative Picard varieties can split Brauer classes using torsors for a fixed abelian scheme.
- The index of an unramified Brauer class divides a fixed power of its period.

## 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.