Flatness testing over singular bases

• Autorzy: Janusz Adamus , Hadi Seyedinejad
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 13H99: None of the above, but in this section
• 13P99: None of the above, but in this section
• 32B99: None of the above, but in this section
• 32S45: Modifications; resolution of singularities
• 13B10: Morphisms
• 13C11: Injective and flat modules and ideals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2013
• Tom: 107
• Numer: 1
• Strony: 87-96

Daty

wydano

2013

Twórcy

autor

Janusz Adamus

• Department of Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B7
• Institute of Mathematics, Faculty of Mathematics, and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland

autor

Hadi Seyedinejad

• Department of Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B7

Identyfikatory

DOI

10.4064/ap107-1-6