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arXiv · 1006.1872

Geometric Auslander criterion for openness of an algebraic morphism

Janusz Adamus·Edward Bierstone·Pierre D. Milman
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Abstract

We give an effective criterion for openness of a morphism of schemes of finite type over a field: Over a normal base of dimension n, failure of openness is detected by a vertical component in the n'th fibred power of the morphism. This is a topological analogue of a criterion for flatness that originates with Auslander.

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Janusz Adamus, Edward Bierstone, Pierre D. Milman. 2017-09-27. Geometric Auslander criterion for openness of an algebraic morphism. https://doi.org/10.1112/blms%2Fbdt028

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