THE COHEN-MACAULAY PROPERTY IN DERIVED COMMUTATIVE ALGEBRA
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
THE COHEN-MACAULAY PROPERTY IN DERIVED COMMUTATIVE ALGEBRA
Original language description
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.
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
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Transactions of the American Mathematical Society
ISSN
0002-9947
e-ISSN
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Volume of the periodical
2020
Issue of the periodical within the volume
373
Country of publishing house
US - UNITED STATES
Number of pages
44
Pages from-to
6095-6138
UT code for WoS article
000574902200002
EID of the result in the Scopus database
2-s2.0-85092314353