Persistence of homology over commutative noetherian rings

2020/05/21 by Avramov, Luchezar L., Iyengar, Srikanth B., Nasseh, Saeed +1 · 3 citations
#13D02 #13D07 (primary) #13D40 (secondary) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2005.10808

Abstract

We describe new classes of noetherian local rings R whose finitely generated modules M have the property that Tor_i^R(M,M)=0 for i≫ 0 implies that M has finite projective dimension, or Extⁱ_R(M,M)=0 for i≫ 0 implies that M has finite projective dimension or finite injective dimension.

Cited by

• On direct summands of syzygies of the residue field of a local ring
• Tor algebra of local rings with decomposable maximal ideal
• On Tor-vanishing of local rings

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