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A fast flatness testing algorithm in characteristic zero. (arXiv:1211.2834v2 [math.AC] UPDATED)
来源于:arXiv
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 the field of reals or
complex numbers, we give a stronger criterion - without the regularity
assumption on R. We also show the corresponding results in the real- and
complex-analytic categories. 查看全文>>