English

The affine class group of a normal scheme

Commutative Algebra 2009-09-29 v1 Algebraic Geometry

Abstract

We study the property of a normal scheme, that the complement of every hypersurface is an affine scheme. To this end we introduce the affine class group. It is a factor group of the divisor class group and measures the deviation from this property. We study the behaviour of the affine class group under faithfully flat extensions and under the formation of products, and we compute it for different classes of rings.

Keywords

Cite

@article{arxiv.math/0209298,
  title  = {The affine class group of a normal scheme},
  author = {Holger Brenner},
  journal= {arXiv preprint arXiv:math/0209298},
  year   = {2009}
}

Comments

to appear in Communications in Algebra

R2 v1 2026-07-22T16:47:51.271Z