Building Modules From the Singular Locus

Authors

  • Jesse Burke
  • Lars Winther Christensen
  • Ryo Takahashi

DOI:

https://doi.org/10.7146/math.scand.a-20449

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.

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Published

2015-03-04

How to Cite

Burke, J., Christensen, L. W., & Takahashi, R. (2015). Building Modules From the Singular Locus. MATHEMATICA SCANDINAVICA, 116(1), 23–33. https://doi.org/10.7146/math.scand.a-20449

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Articles