Finitistic dimensions over commutative DG-rings

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10505575" target="_blank" >RIV/00216208:11320/25:10505575 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=68EPuQPa1d" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=68EPuQPa1d</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00209-024-03617-2" target="_blank" >10.1007/s00209-024-03617-2</a>

Result language
angličtina
Original language name
Finitistic dimensions over commutative DG-rings
Original language description
In this paper we study the finitistic dimensions of commutative noetherian non-positive DG-rings with finite amplitude. We prove that any DG-module M of finite flat dimension over such a DG-ring satisfies projdimA(M)<= dim(H0(A))-inf(M)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${textrm{proj},textrm{dim}}_A(M) le dim (textrm{H}<^>0 (A)) - inf (M)$$end{document}. We further provide explicit constructions of DG-modules with prescribed projective dimension and deduce that the big finitistic projective dimension satisfies the bounds dim(H0(A))-amp(A)<= FPD(A)<= dim(H0(A))documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$dim (textrm{H}<^>0 (A)) - {text {amp}}(A) le textsf{FPD}(A) le dim (textrm{H}<^>0(A))$$end{document}. Moreover, we prove that DG-rings exist which achieve either bound. As a direct application, we prove new vanishing results for the derived Hochschild (co)homology of homologically smooth algebras.
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
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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