The Differential Brauer Group

2010/03/06 by Raymond T. Hoobler, Hoobler, Raymond T.
Computer Science · Mathematics · #14F20 #16K50 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1003.1421

openalex publication_date 2010/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a ring equipped with a derivation δ. We study differential Azumaya A algebras, that is, Azumaya A algebras equipped with a derivation that extends δ. We calculate the differential automorphism group of the trivial differential algebra, M_n(A) with coordinatewise differentiation. We introduce the δ-flat Grothendieck topology to show that any differential Azumaya A algebra is locally isomorphic to a trivial one and then construct, as in the non-differential setting, the embedding of the differential Brauer group into H²(A_δ-pl,G_m,δ) . We conclude by showing that the differential Brauer group coincides with the usual Brauer group in the affine setting.

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