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Moduli of étale subalgebras in an Azumaya algebra

Daniel Krashen
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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 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.

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Daniel Krashen. 2004-11-24. Moduli of étale subalgebras in an Azumaya algebra. https://arxiv.org/abs/math/0411529

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