The Brauer-Clifford group for locally finite (S, H)-Azumaya algebras

Abstract

In this article, we define the notion of Brauer-Clifford group for H-locally finite (S, H)-Azumaya algebras, when H is a cocommutative Hopf algebra and S is an H-locally finite commutative H-module algebra over a commutative noetherian ring k. This is the situation that arises in applications with connections to algebraic geometry. This Brauer-Clifford group turns out to be an example of a Brauer group of a symmetric monoidal category.