A generalized Dade's Lemma for local rings
Commutative Algebra
2017-12-01 v2
Abstract
We prove a generalized Dade's Lemma for quotients of local rings by ideals generated by regular sequences. That is, given a pair of finitely generated modules over such a ring with algebraically closed residue field, we prove a sufficient (and necessary) condition for the vanishing of all higher Ext or Tor of the modules. This condition involves the vanishing of all higher Ext or Tor of the modules over all quotients by a minimal generator of the ideal generated by the regular sequence.
Cite
@article{arxiv.1601.01238,
title = {A generalized Dade's Lemma for local rings},
author = {Petter Andreas Bergh and David A. Jorgensen},
journal= {arXiv preprint arXiv:1601.01238},
year = {2017}
}