The (ir)regularity of Tor and Ext

Chardin, Marc and Ghosh, Dipankar and Nemati, Navid (2021) The (ir)regularity of Tor and Ext. Transactions of the American Mathematical Society, 375 (01). pp. 47-70. ISSN 0002-9947

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We investigate the asymptotic behavior of Castelnuovo-Mumford regularity of Ext and Tor, with respect to the homological degree, over complete intersection rings. We derive from a theorem of Gulliksen a linearity result for the regularity of Ext modules in high homological degrees. We show a similar result for Tor, under the additional hypothesis that high enough Tor modules are supported in dimension at most one; we then provide examples showing that the behavior could be pretty hectic when the latter condition is not satisfied. © 2021 American Mathematical Society

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Item Type: Article
Uncontrolled Keywords: Asymptotic behavior; Castelnuovo-Mumford regularity; Complete intersection rings; Eisenbud operators; Ext; Spectral sequences; Tor
Subjects: Mathematics
Divisions: Department of Mathematics
Depositing User: . LibTrainee 2021
Date Deposited: 25 Jul 2022 11:27
Last Modified: 25 Jul 2022 11:27
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