Galois descent for higher Brauer groups

TL;DR

This paper explores Galois descent for higher Brauer groups on smooth projective varieties, extending known finiteness results to these more complex algebraic structures.

Contribution

It extends a finiteness result of Colliot-Thélène and Skorobogatov to higher Brauer groups, advancing understanding of their Galois descent properties.

Findings

Extended finiteness results to higher Brauer groups.

Provided new insights into Galois descent for algebraic varieties.

Enhanced the theoretical framework for higher Brauer groups.

Abstract

For $X$ a smooth projective variety over a field $k$, we consider the problem of Galois descent for higher Brauer groups. More precisely, we extend a finiteness result of Colliot-Th\'el\`ene and Skorobogatov to higher Brauer groups.