The vanishing of Tor1R(R+,k) implies that R is regular
Ian M. Aberbach
Abstract
Let (R,m,k) be an excellent local ring of positive prime characteristic. We show that if Tor1R(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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