Smooth flat maps over commutative DG-rings

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10436301" target="_blank" >RIV/00216208:11320/21:10436301 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=b3Fok0pqke" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=b3Fok0pqke</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00209-021-02748-0" target="_blank" >10.1007/s00209-021-02748-0</a>

Result language
angličtina
Original language name
Smooth flat maps over commutative DG-rings
Original language description
We study smooth maps that arise in derived algebraic geometry. Given a map A -> B between non-positive commutative noetherian DG-rings which is of flat dimension 0, we show that it is smooth in the sense of Toen-Vezzosi if and only if it is homologically smooth in the sense of Kontsevich. We then show that B, being a perfect DG-module over B circle times(L)(A) B has, locally, an explicit semi-free resolution as a Koszul complex. As an application we show that a strong form of Van den Bergh duality between (derived) Hochschild homology and cohomology holds in this setting.
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
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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