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arXiv · 1905.02375

The (ir)regularity of Tor and Ext

Marc Chardin·Dipankar Ghosh·Navid Nemati
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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.

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Marc Chardin, Dipankar Ghosh, Navid Nemati. 2019-05-07. The (ir)regularity of Tor and Ext. https://doi.org/10.1090/tran%2F8429

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