The vanishing of Tor₁^R(R⁺,k) implies that R is regular

2003/09/16 by Ian M. Aberbach, Aberbach, Ian M.
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Finite Group Theory Research #Polynomial and algebraic computation #math.AC #msc:13A35 #msc:13H05

paper · pdf · doi:10.48550/arxiv.math/0309267

3 pages, to appear in Proceedings of the AMS

arxiv created 2003/09/16 · arxiv updated 2009/12/01

Abstract

Let (R,m,k) be an excellent local ring of positive prime characteristic. We show that if Tor₁^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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