Homologically Smooth Connected Cochain DGAs

Let A be a connected cochain DG algebra such that H ( A ) is a Noetherian graded algebra. We give some criteria for A to be homologically smooth in terms of the singularity category, the cone length of the canonical module k and the global dimension of A . For any cohomologically finite DG A -module...

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Bibliographic Details
Published inAlgebras and representation theory Vol. 27; no. 5; pp. 1931 - 1955
Main Author Mao, X.-F.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 2024
Springer Nature B.V
Subjects
Algebra
Associative Rings and Algebras
Commutative Rings and Algebras
Mathematics
Mathematics and Statistics
Modules
Non-associative Rings and Algebras
Regularity
16W50
16E65
Castelnuovo-Mumford regularity
Cone length
Global dimension
Homologically smooth
Primary 16E10
16E45
DG algebra
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Summary:Let A be a connected cochain DG algebra such that H ( A ) is a Noetherian graded algebra. We give some criteria for A to be homologically smooth in terms of the singularity category, the cone length of the canonical module k and the global dimension of A . For any cohomologically finite DG A -module M , we show that it is compact when A is homologically smooth. If A is in addition Gorenstein, we get CMreg M = depth A A + Ext . reg M < ∞ , where CMreg M is the Castelnuovo-Mumford regularity of M , depth A A is the depth of A and Ext . reg M is the Ext-regularity of M .
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-024-10287-5