Moduli of étale subalgebras in an Azumaya algebra

Details Moduli of étale subalgebras in an Azumaya algebra Moduli of étale subalgebras in an Azumaya algebra

2004-11-24

arxiv.org/abs/math/0411529v1

Mathematics

Rings and Algebras

8 pages

Scientific paper

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.

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