Sequence-regular commutative DG-rings

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10488007" target="_blank" >RIV/00216208:11320/24:10488007 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xiH6iZ8z94" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=xiH6iZ8z94</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jalgebra.2024.02.034" target="_blank" >10.1016/j.jalgebra.2024.02.034</a>

Result language
angličtina
Original language name
Sequence-regular commutative DG-rings
Original language description
We introduce a new class of commutative noetherian DGrings which generalizes the class of regular local rings. These are defined to be local DG -rings (A, m<overline>) such that the maximal ideal m<overline> subset of H0(A) can be generated by an A -regular sequence. We call these DG -rings sequence -regular DG -rings, and make a detailed study of them. Using methods of Cohen -Macaulay differential graded algebra, we prove that the AuslanderBuchsbaum-Serre theorem about localization generalizes to this setting. This allows us to define global sequence -regular DG -rings, and to introduce this regularity condition to derived algebraic geometry. It is shown that these DG -rings share many properties of classical regular local rings, and in particular we are able to construct canonical residue DGfields in this context. Finally, we show that sequence -regular DG -rings are ubiquitous, and in particular, any eventually coconnective derived algebraic variety over a perfect field is generically sequence -regular. (c) 2024 Elsevier Inc. All rights reserved.
Czech name
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Czech description
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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

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)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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