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Flatness testing over singular bases

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Adamus J., Seyedinejad H.

Annales Polonici Mathematici

2013

tom 107

nr 1

87-96

We show that non-flatness of a morphism φ:X→ Y of complex-analytic spaces with a locally irreducible target of dimension n manifests in the existence of vertical components in the n-fold fibred power of the pull-back of φ to the desingularization of Y. An algebraic analogue follows: Let R be a locally (analytically) irreducible finite type ℂ-algebra and an integral domain of Krull dimension n, and let S be a regular n-dimensional algebra of finite type over R (but not necessarily a finite R-module), such that Spec S → Spec R is dominant. Then a finite type R-algebra A is R-flat if and only if $(A^{⊗i^n_R})⊗_R S$ is a torsion-free R-module.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Adamus J.

1 Seyedinejad H.

1 2013

Wyniki wyszukiwania

Flatness testing over singular bases