Koszul complexes over Cohen-Macaulay rings

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10436408" target="_blank" >RIV/00216208:11320/21:10436408 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pg7zEt10-Y" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pg7zEt10-Y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2021.107806" target="_blank" >10.1016/j.aim.2021.107806</a>

Result language
angličtina
Original language name
Koszul complexes over Cohen-Macaulay rings
Original language description
We prove a Cohen-Macaulay version of a result by Avramov-Golod and Frankild-Jorgensen about Gorenstein rings, showing that if a noetherian ring A is Cohen-Macaulay, and a(1), ..., a(n) is any sequence of elements in A, then the Koszul complex K(A; a(1), ..., a(n)) is a Cohen-Macaulay DG-ring. We further generalize this result, showing that it also holds for commutative DG-rings. In the process of proving this, we develop a new technique to study the dimension theory of a noetherian ring A, by finding a Cohen-Macaulay DG-ring B such that H-0 (B) = A, and using the Cohen-Macaulay structure of B to deduce results about A. As application, we prove that if f : X -> Y is a morphism of schemes, where X is Cohen-Macaulay and Y is nonsingular, then the homotopy fiber of f at every point is Cohen-Macaulay. As another application, we generalize the miracle flatness theorem. Generalizations of these applications to derived algebraic geometry are also given. (C) 2021 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
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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
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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