English

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.

Keywords

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

R2 v1 2026-07-22T16:32:00.947Z