Open loci results for commutative DG-rings
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10453398" target="_blank" >RIV/00216208:11320/22:10453398 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=JeZ-NNB319" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=JeZ-NNB319</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2021.106922" target="_blank" >10.1016/j.jpaa.2021.106922</a>
Alternative languages
Result language
angličtina
Original language name
Open loci results for commutative DG-rings
Original language description
Given a commutative noetherian non-positive DG-ring with bounded cohomology which has a dualizing DG-mo dule, we study its regular, Gorenstein and Cohen-Macaulay loci. We give a sufficient condition for the regular locus to be open, and show that the Gorenstein locus is always open. However, both of these loci are often empty: we show that no matter how nice H-0(A) is, there are examples where the Gorenstein locus of A is empty. We then show that the Cohen-Macaulay locus of a commutative noetherian DG-ring with bounded cohomology which has a dualizing DG-mo dule always contains a dense open set. Our results imply that under mild hypothesis, eventually coconnective locally noetherian derived schemes are generically Cohen-Macaulay, but even in very nice cases, they need not be generically Gorenstein. (c) 2021 Elsevier B.V. All rights reserved.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GJ20-02760Y" target="_blank" >GJ20-02760Y: Cohen-Macaulay rings and their applications in higher algebra and topology</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Pure and Applied Algebra
ISSN
0022-4049
e-ISSN
1873-1376
Volume of the periodical
226
Issue of the periodical within the volume
5
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
11
Pages from-to
106922
UT code for WoS article
000711624500005
EID of the result in the Scopus database
2-s2.0-85117238668