Cohomological jump loci and duality in local algebra
File(s)
Accepted version
Author(s)
Briggs, Benjamin
McCormick, Daniel
Pollitz, Josh
Type
Journal Article
Abstract
In this article a higher order support theory, called the cohomological jump loci, is introduced and studied for dg modules over a Koszul extension of a local dg algebra. The generality of this setting applies to dg modules over local complete intersection rings, exterior algebras and certain group algebras in prime characteristic. This family of varieties generalizes the well-studied support varieties in each of these contexts. We show that cohomological jump loci satisfy several interesting properties, including being closed under (Grothendieck) duality. The main application of this support theory is that over a local ring the homological invariants of Betti degree and complexity are preserved under duality for finitely generated modules having finite complete intersection dimension.
Date Issued
2023-06
Date Acceptance
2023-04-05
Citation
Mathematische Zeitschrift, 2023, 304 (2)
ISSN
0025-5874
Publisher
Springer Science and Business Media LLC
Journal / Book Title
Mathematische Zeitschrift
Volume
304
Issue
2
Copyright Statement
Copyright © 2024 Springer-Verlag. This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00209-023-03276-9
Identifier
http://dx.doi.org/10.1007/s00209-023-03276-9
Publication Status
Published
Article Number
30
Date Publish Online
2023-05-13