A Generalized Dade’s Lemma for Local Rings

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...

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Bibliographic Details
Published in:Algebras and representation theory 2018-12, Vol.21 (6), p.1369-1380
Main Authors: Bergh, Petter Andreas, Jorgensen, David A.
Format: Article
Language:English
Subjects:
Associative Rings and Algebras
Commutative Rings and Algebras
Mathematics
Mathematics and Statistics
Modules
Non-associative Rings and Algebras
Quotients
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Summary: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.
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-017-9751-7