Moduli of \'etale subalgebras in an Azumaya algebra

Abstract

Let $A$ be a sheaf of Azumaya algebras over a Noetherian base $S$. In this paper we describe using generalized Severi-Brauer varieties, a quasi-projective moduli space parametrizing sheaves of \`etale subalgebras of $A$. In the case that $S$ is the spectrum of a field, we study the geometry of this moduli space, and show that in certain cases it is a rational variety.