The prime divisors of the period and index of a Brauer class

Abstract

We show that in locally-ringed connected topoi the primes dividing the period and index of a Brauer class coincide. The result applies in particular to Brauer classes on connected schemes, algebraic stacks, topological spaces and to the projective representation theory of profinite groups.

This is a concise version. A longer version exists, the additions being largely background material on topoi that the authors had to teach themselves in order to write the paper. It may be obtained on the second-named author's website, and possibly elsewhere