An inductive analytic criterion for flatness

Details An inductive analytic criterion for flatness An inductive analytic criterion for flatness

2011-01-10

arxiv.org/abs/1101.1938v1

Mathematics

Commutative Algebra

11 pages

Scientific paper

We present a constructive criterion for flatness of a morphism of analytic spaces X -> Y or, more generally, for flatness over Y of a coherent sheaf of modules on X. The criterion is a combination of a simple linear-algebra condition "in codimension zero" and a condition "in codimension one" which can be used together with the Weierstrass preparation theorem to inductively reduce the fibre dimension of the morphism.

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