The (ir)regularity of Tor and Ext

Abstract

We investigate the asymptotic behaviour 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 behaviour could be pretty hectic when the latter condition is not satisfied.Comment: 24 pages, Comments and suggestions are welcom