There are enough Azumaya algebras on surfaces
Copyright policy )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.
13 pages, major revision, to appear in Math. Ann
- Ruhr University Bochum Germany
normal algebraic surfaces, Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), cohomological Brauer group, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Mathematics - Algebraic Geometry, FOS: Mathematics, nonfree vector bundles, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Algebraic Geometry (math.AG), Brauer groups of schemes, 13A20, 14J17,14J60, 16H05
normal algebraic surfaces, Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), cohomological Brauer group, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Mathematics - Algebraic Geometry, FOS: Mathematics, nonfree vector bundles, Vector bundles on surfaces and higher-dimensional varieties, and their moduli, Algebraic Geometry (math.AG), Brauer groups of schemes, 13A20, 14J17,14J60, 16H05
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