There are enough Azumaya algebras on surfaces

Details There are enough Azumaya algebras on surfaces There are enough Azumaya algebras on surfaces

2000-03-31

arxiv.org/abs/math/0003229v2

Math. Ann. 321 (2001), 439--454

Mathematics

Algebraic Geometry

13 pages, major revision, to appear in Math. Ann

Scientific paper

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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