The vanishing of Tor_1^R(R^+,k) implies that R is regular
Commutative Algebra
2007-05-23 v1
Abstract
Let (R,m,k) be an excellent local ring of positive prime characteristic. We show that if Tor_1^R(R^+,k) = 0 then R is regular. This improves a result of Schoutens, in which the additional hypothesis that R was an isolated singularity was required for the proof.
Cite
@article{arxiv.math/0309267,
title = {The vanishing of Tor_1^R(R^+,k) implies that R is regular},
author = {Ian M. Aberbach},
journal= {arXiv preprint arXiv:math/0309267},
year = {2007}
}
Comments
3 pages, to appear in Proceedings of the AMS