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Constructing nonproxy small test modules for the complete intersection property
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2009.11800v3.pdf | Accepted version | 261.76 kB | Adobe PDF | View/Open |
Title: | Constructing nonproxy small test modules for the complete intersection property |
Authors: | BRIGGS, B GRIFO, E POLLITZ, J |
Item Type: | Journal Article |
Abstract: | A local ring R is regular if and only if every finitely generated R-module has finite projective dimension. Moreover, the residue field k is a test module: R is regular if and only if k has finite projective dimension. This characterization can be extended to the bounded derived category Df (R), which contains only small objects if and only if R is regular. Recent results of Pollitz, completing work initiated by Dwyer-Greenlees-Iyengar, yield an analogous characterization for complete intersections: R is a complete intersection if and only if every object in Df (R) is proxy small. In this paper, we study a return to the world of R-modules, and search for finitely generated R-modules that are not proxy small whenever R is not a complete intersection. We give an algorithm to construct such modules in certain settings, including over equipresented rings and Stanley-Reisner rings. |
Issue Date: | Jun-2022 |
Date of Acceptance: | 1-Jun-2021 |
URI: | http://hdl.handle.net/10044/1/114004 |
DOI: | 10.1017/nmj.2021.7 |
ISSN: | 0027-7630 |
Publisher: | Cambridge University Press |
Start Page: | 412 |
End Page: | 429 |
Journal / Book Title: | Nagoya Mathematical Journal |
Volume: | 246 |
Copyright Statement: | © (2021) The Authors. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license. This is the author’s accepted manuscript made available under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Publication Status: | Published |
Online Publication Date: | 2021-06-21 |
Appears in Collections: | Pure Mathematics Mathematics |
This item is licensed under a Creative Commons License