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- W4300605675 abstract "Given an essentially finite type morphism of schemes f: X --> Y and a positive integer d, let f^{d}: X^{d} --> Y denote the natural map from the d-fold fiber product, X^{d}, of X over Y and pi_i: X^{d} --> X the i'th canonical projection. When Y smooth over a field and F is a coherent sheaf on X, it is proved that F is flat over Y if (and only if) f^{d} maps the associated points of the tensor product sheaf otimes_{i=1}^d pi_i^*(F) to generic points of Y, for some d greater than or equal to dim Y. The equivalent statement in commutative algebra is an analog---but not a consequence---of a classical criterion of Auslander and Lichtenbaum for the freeness of finitely generated modules over regular local rings." @default.
- W4300605675 created "2022-10-03" @default.
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- W4300605675 date "2010-02-18" @default.
- W4300605675 modified "2023-10-18" @default.
- W4300605675 title "Detecting flatness over smooth bases" @default.
- W4300605675 doi "https://doi.org/10.48550/arxiv.1002.3652" @default.
- W4300605675 hasPublicationYear "2010" @default.
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