Open loci results for commutative DG-rings

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Open loci results for commutative DG-rings

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Open loci results for commutative DG-rings

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ20-02760Y" target="_blank" >GJ20-02760Y: Cohen-Macaulayovy okruhy a jejich aplikace ve vyšší algebře a topologii</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Pure and Applied Algebra

ISSN

0022-4049

e-ISSN

1873-1376

Svazek periodika

226

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

11

Strana od-do

106922

Kód UT WoS článku

000711624500005

EID výsledku v databázi Scopus

2-s2.0-85117238668