English

The structure of quasi-complete intersection ideals

Commutative Algebra 2018-10-01 v1

Abstract

We prove that every quasi-complete intersection ideal is obtained from a pair of nested complete intersection ideals by way of a flat base change. As a by-product we establish a rigidity statement for the minimal two-step Tate complex associated to an ideal II in a local ring RR. Furthermore, we define a minimal two-step complete Tate complex TT for each ideal II in a local ring RR; and prove a rigidity result for it. The complex TT is exact if and only if II is a quasi-complete intersection ideal; and in this case, TT is the minimal complete resolution of R/IR/I by free RR-modules.

Keywords

Cite

@article{arxiv.1809.11094,
  title  = {The structure of quasi-complete intersection ideals},
  author = {Andrew R. Kustin and Liana M. Sega},
  journal= {arXiv preprint arXiv:1809.11094},
  year   = {2018}
}
R2 v1 2026-06-23T04:22:13.776Z