Die Brauersche Gruppe; ihre Verallgemeinerungen und Anwendungen in der arithmetischen Geometrie

TL;DR

This survey reviews the Brauersche group, its generalizations, and applications in arithmetic geometry, highlighting its relevance to the period-index problem for central simple algebras, as discussed in a 2001 conference.

Contribution

It provides a comprehensive overview of the Brauersche group and its extensions, connecting classical theory with recent developments in arithmetic geometry.

Findings

Connections between Brauersche groups and the period-index problem

Recent applications in arithmetic geometry

Unpublished survey cited in current research

Abstract

This is an unchanged version of an unpublished, ``state of the art'' survey given at a conference held in Stuttgart in 2001 to celebrate the 100th birthday of Richard Brauer. This text was recently quoted in several papers on the period-index problem for central simple algebras.