Building modules from the singular locus
Commutative Algebra
2014-11-20 v3
Abstract
A finitely generated module over a commutative noetherian ring of finite Krull dimension can be built from the prime ideals in the singular locus by iteration of three procedures: taking extensions, direct summands, and cosyzygies. In 2003 Schoutens gave a bound on the number of iterations required to build any module, and in this note we determine the exact number. This building process yields a stratification of the module category, which we study in detail for local rings that have an isolated singularity.
Keywords
Cite
@article{arxiv.1210.0055,
title = {Building modules from the singular locus},
author = {Jesse Burke and Lars Winther Christensen and Ryo Takahashi},
journal= {arXiv preprint arXiv:1210.0055},
year = {2014}
}
Comments
Minor corrections; final version to appear in Math. Scand; 8 pp