The period-index problem for fields of transcendence degree 2

TL;DR

This paper proves the standard period-index conjecture for the Brauer group of certain fields using geometric methods, specifically for fields of transcendence degree 2 over finite fields.

Contribution

It establishes the conjecture in a new setting by applying geometric techniques to fields of transcendence degree 2 over finite fields.

Findings

Proves the period-index conjecture for these fields.

Demonstrates the effectiveness of geometric methods in this context.

Advances understanding of the Brauer group in algebraic geometry.

Abstract

Using geometric methods we prove the standard period-index conjecture for the Brauer group of a field of transcendence degree 2 over a finite field.