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Vertical components and flatness of Nash mappings

Authors
Journal
Journal of Pure and Applied Algebra
0022-4049
Publisher
Elsevier
Publication Date
Volume
193
Identifiers
DOI: 10.1016/j.jpaa.2004.02.009

Abstract

Abstract We prove the following criterion for flatness of Nash morphisms: Let f ξ : X ξ→Y η be a Nash morphism of reduced Nash germs with X ξ of pure dimension and Y η smooth of dimension n. Then f ξ is flat if and only if the nth analytic tensor power O X,ξ ⊗ ̂ O Y,η ⋯ ⊗ ̂ O Y,η O X,ξ n times is a torsion-free O Y,η -module.

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