Homology over trivial extensions of commutative DG algebras

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

Homology over trivial extensions of commutative DG algebras

Commutative Algebra 2015-08-05 v1

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

Abstract

Conditions on the Koszul complex of a noetherian local ring $R$ guarantee that $\mathrm{Tor}^{R}_{i}(M,N)$ is non-zero 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.

Keywords

trivial extension commutative differential graded algebra Koszul complex Tor homology noetherian local ring finitely generated module

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@article{arxiv.1508.00748,
  title  = {Homology over trivial extensions of commutative DG algebras},
  author = {Luchezar L. Avramov and Srikanth B. Iyengar and Saeed Nasseh and Sean Sather-Wagstaff},
  journal= {arXiv preprint arXiv:1508.00748},
  year   = {2015}
}

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14 pages

Homology over trivial extensions of commutative DG algebras

Abstract

Keywords

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