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A fast flatness testing criterion in characteristic zero

2015
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Proceedings of the American Mathematical Society
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We prove a fast computable criterion that expresses non-flatness in terms of torsion: Let R be a regular algebra of finite type over a field K of characteristic zero and let F be a module finitely generated over an R-algebra of finite type. Given a maximal ideal m in R, let S be the coordinate ring of the blowing-up of Spec(R) at the closed point m. Then F is flat over R localized in m if and only if the tensor product of F with S over R is a torsion-free module over R localized in m. If K is

doi:10.1090/s0002-9939-2015-12463-x
fatcat:e4g2jwjnnjfapdcehp2qt7fvnq