Homology over trivial extensions of commutative DG algebras

Luchezar L. Avramov; Srikanth B. Iyengar; Saeed Nasseh; Sean Sather-Wagstaff

doi:10.1080/00927872.2018.1472272

Homology over trivial extensions of commutative DG algebras

Luchezar L. Avramov
, Srikanth B. Iyengar
, Saeed Nasseh
, Sean Sather-Wagstaff

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

Conditions on the Koszul complex of a noetherian local ring R guarantee that Tor^R _i(M,N) is nonzero for infinitely many i, when M and N are finitely generated R-modules of infinite projective dimension. These conditions are obtained from results concerning Tor of differential graded modules over certain trivial extensions of commutative differential graded algebras. Dedicated to Gennady Lyubeznik on the occasion of his 60th birthday.

Original language	English
Pages (from-to)	2341-2356
Number of pages	16
Journal	Communications in Algebra
Volume	47
Issue number	6
DOIs	https://doi.org/10.1080/00927872.2018.1472272
State	Published - Jun 3 2019

Scopus Subject Areas

Algebra and Number Theory

Keywords

Local DG algebra
perfect DG module
vanishing of Tor

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10.1080/00927872.2018.1472272

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abstract = "Conditions on the Koszul complex of a noetherian local ring R guarantee that TorR i(M,N) is nonzero for infinitely many i, when M and N are finitely generated R-modules of infinite projective dimension. These conditions are obtained from results concerning Tor of differential graded modules over certain trivial extensions of commutative differential graded algebras. Dedicated to Gennady Lyubeznik on the occasion of his 60th birthday.",

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AU - Avramov, Luchezar L.

AU - Iyengar, Srikanth B.

AU - Nasseh, Saeed

AU - Sather-Wagstaff, Sean

PY - 2019/6/3

Y1 - 2019/6/3

N2 - Conditions on the Koszul complex of a noetherian local ring R guarantee that TorR i(M,N) is nonzero for infinitely many i, when M and N are finitely generated R-modules of infinite projective dimension. These conditions are obtained from results concerning Tor of differential graded modules over certain trivial extensions of commutative differential graded algebras. Dedicated to Gennady Lyubeznik on the occasion of his 60th birthday.

AB - Conditions on the Koszul complex of a noetherian local ring R guarantee that TorR i(M,N) is nonzero for infinitely many i, when M and N are finitely generated R-modules of infinite projective dimension. These conditions are obtained from results concerning Tor of differential graded modules over certain trivial extensions of commutative differential graded algebras. Dedicated to Gennady Lyubeznik on the occasion of his 60th birthday.

KW - Local DG algebra

KW - perfect DG module

KW - vanishing of Tor

UR - https://www.scopus.com/pages/publications/85060172947

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DO - 10.1080/00927872.2018.1472272

M3 - Article

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SP - 2341

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JO - Communications in Algebra

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Homology over trivial extensions of commutative DG algebras

Abstract

Scopus Subject Areas

Keywords

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