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

Ian M. Aberbach
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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.

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Ian M. Aberbach. 2003-09-16. The vanishing of Tor_1^R(R^+,k) implies that R is regular. https://arxiv.org/abs/math/0309267

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