There are enough Azumaya algebras on surfaces

2000/03/31 by Stefan Schroeer
Mathematics · #math.AG #math.AC #msc:13A20 #msc:14J17 #msc:14J60 #msc:16H05

paper · pdf

published as Math. Ann. 321 (2001), 439--454 · 13 pages, major revision, to appear in Math. Ann

arxiv created 2001/04/04 · arxiv updated 2009/11/30

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.

Related

• The Brauer group of analytic K3 surfaces
• Surfaces defined by pairs of polynomials
• Azumaya algebras over unramified extensions of function fields
• Brauer groups and quotient stacks
• Enriques surfaces with trivial Brauer map and involutions on hyperkähler manifolds