English

On the homology of regular quotients

Commutative Algebra 2013-05-13 v1 Algebraic Topology

Abstract

We construct a free resolution of R/IsR/I^s over RR where I\idealRI\ideal R is generated by a (finite or infinite) regular sequence. This generalizes the Koszul complex for the case s=1s=1. For s>1s>1, we easily deduce that the algebra structure of \TorR(R/I,R/Is)\Tor^R_*(R/I,R/I^s) is trivial and the reduction map R/Is\lraR/Is1R/I^s\lra R/I^{s-1} induces the trivial map of algebras.

Keywords

Cite

@article{arxiv.1305.2216,
  title  = {On the homology of regular quotients},
  author = {Andrew Baker},
  journal= {arXiv preprint arXiv:1305.2216},
  year   = {2013}
}