Moduli of étale subalgebras in an Azumaya algebra
Abstract
Description
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 ètale 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.
8 pages
8 pages