The (ir)regularity of Tor and Ext

Chardin, Marc; Ghosh, Dipankar; Nemati, Navid

doi:10.1090/tran/8429

The (ir)regularity of Tor and Ext
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by Marc Chardin, Dipankar Ghosh and Navid Nemati PDF

Trans. Amer. Math. Soc. 375 (2022), 47-70 Request permission

Abstract:

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.

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