There are enough Azumaya algebras on surfaces
Algebraic Geometry
2007-05-23 v2 Commutative Algebra
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.
Cite
@article{arxiv.math/0003229,
title = {There are enough Azumaya algebras on surfaces},
author = {Stefan Schroeer},
journal= {arXiv preprint arXiv:math/0003229},
year = {2007}
}
Comments
13 pages, major revision, to appear in Math. Ann