A Generalized Dade’s Lemma for Local Rings
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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.
KeywordsRegular sequences Local rings Dade’s Lemma
Mathematics Subject Classification (2010)13D02 13D07
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