The vanishing of Tor_1^R(R^+,k) implies that R is regular

Details The vanishing of Tor_1^R(R^+,k) implies that R is regular The vanishing of Tor_1^R(R^+,k) implies that R is regular

2003-09-16

arxiv.org/abs/math/0309267v1

Mathematics

Commutative Algebra

3 pages, to appear in Proceedings of the AMS

Scientific paper

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.

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