# 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.

## Key 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.