THE COHEN-MACAULAY PROPERTY IN DERIVED COMMUTATIVE ALGEBRA

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10423963" target="_blank" >RIV/00216208:11320/20:10423963 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=OqZRDtRuo-" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=OqZRDtRuo-</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1090/tran/8099" target="_blank" >10.1090/tran/8099</a>

Jazyk výsledku

angličtina

Název v původním jazyce

THE COHEN-MACAULAY PROPERTY IN DERIVED COMMUTATIVE ALGEBRA

Popis výsledku v původním jazyce

By extending some basic results of Grothendieck and Foxby about local cohomology to commutative DG-rings, we prove new amplitude inequalities about finite DG-modules of finite injective dimension over commutative local DG-rings, complementing results of Jorgensen and resolving a recent conjecture of Minamoto. When these inequalities are equalities, we arrive at the notion of a local-Cohen-Macaulay DG-ring. We make a detailed study of this notion, showing that much of the classical theory of Cohen-Macaulay rings and modules can be generalized to the derived setting, and that there are many natural examples of local-Cohen-Macaulay DG-rings. In particular, local Gorenstein DG-rings are local-Cohen-Macaulay. Our work is in a non-positive cohomological situation, allowing the Cohen-Macaulay condition to be introduced to derived algebraic geometry, but we also discuss extensions of it to non-negative DG-rings, which could lead to the concept of Cohen-Macaulayness in topology.

Název v anglickém jazyce

THE COHEN-MACAULAY PROPERTY IN DERIVED COMMUTATIVE ALGEBRA

Popis výsledku anglicky

By extending some basic results of Grothendieck and Foxby about local cohomology to commutative DG-rings, we prove new amplitude inequalities about finite DG-modules of finite injective dimension over commutative local DG-rings, complementing results of Jorgensen and resolving a recent conjecture of Minamoto. When these inequalities are equalities, we arrive at the notion of a local-Cohen-Macaulay DG-ring. We make a detailed study of this notion, showing that much of the classical theory of Cohen-Macaulay rings and modules can be generalized to the derived setting, and that there are many natural examples of local-Cohen-Macaulay DG-rings. In particular, local Gorenstein DG-rings are local-Cohen-Macaulay. Our work is in a non-positive cohomological situation, allowing the Cohen-Macaulay condition to be introduced to derived algebraic geometry, but we also discuss extensions of it to non-negative DG-rings, which could lead to the concept of Cohen-Macaulayness in topology.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Transactions of the American Mathematical Society

ISSN

0002-9947

e-ISSN

—

Svazek periodika

2020

Číslo periodika v rámci svazku

373

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

44

Strana od-do

6095-6138

Kód UT WoS článku

000574902200002

EID výsledku v databázi Scopus

2-s2.0-85092314353