On the homology of regular quotients
arXiv:1305.2216
Abstract
We construct a free resolution of over where $I\ideal R$ is generated by a (finite or infinite) regular sequence. This generalizes the Koszul complex for the case . For , we easily deduce that the algebra structure of $\Tor^R_*(R/I,R/I^s)$ is trivial and the reduction map $R/I^s\lra R/I^{s-1}$ induces the trivial map of algebras.