Prime decomposition for the index of a Brauer class

TL;DR

This paper proves that the index of a Brauer class can be decomposed into prime factors over any base scheme, highlighting a fundamental property of Brauer classes distinct from Azumaya algebras.

Contribution

It establishes the prime decomposition property for the index of Brauer classes over general base schemes, contrasting with prior results on Azumaya algebras.

Findings

Index of a Brauer class admits prime decomposition over any base scheme

Contrasts with the non-decomposability of Azumaya algebras

Provides new insights into the structure of Brauer classes

Abstract

We prove that the index of a Brauer class satisfies prime decomposition over a general base scheme. This contrasts with our previous result that there is no general prime decomposition of Azumaya algebras.