Group Rings which are Azumaya Algebras

There Are Enough Azumaya Algebras on Surfaces

Using Maruyama’s theory of elementary transformations, I show that the Brauer group surjects onto the cohomological Brauer group for separated geometrically normal algebraic surfaces. As an application, I infer the existence of nonfree vector bundles on proper normal algebraic surfaces.

On Azumaya Galois Extensions and Skew Group Rings

Two characterizations of an Azumaya Galois extension of a ring are given in terms of the Azumaya skew group ring of the Galois group over the extension and a Galois extension of a ring with a special Galois system is determined by the trace of the Galois group.

Azumaya algebras and derivations

Motives of Azumaya Algebras

We study the slice filtration for the K-theory of a sheaf of Azumaya algebras A, and for the motive of a Severi-Brauer variety, the latter in the case of a central simple algebra of prime degree over a field. Using the Beilinson-Lichtenbaum conjecture, we apply our results to show the vanishing of SK2(A) for a central simple algebra A of square-free index (prime to the characteristic). This pro...

Deformations of Azumaya Algebras

In this paper we compute the deformation theory of a special class of algebras, namely of Azumaya algebras on a manifold (C or complex analytic). Deformation theory of associative algebras was initiated by Gerstenhaber in [G]. A deformation of an associative algebra A over an Artinian ring a is an a-linear associative algebra structure on A⊗ a such that, for the maximal ideal m of a, A ⊗ m is a...