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There are enough Azumaya algebras on surfaces

Stefan Schroeer
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Abstract

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.

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Stefan Schroeer. 2001-04-04. There are enough Azumaya algebras on surfaces. https://arxiv.org/abs/math/0003229

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