Unramified Morphism

(Algebraic Geometry)


Algebraic Geometry
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What is Unramified morphism?

In algebraic geometry, an unramified morphism is a morphism of schemes such that (a) it is locally of finite presentation and (b) for each and , we have that 1. * The residue field is a separable algebraic extension of . 2. * where and are maximal ideals of the local rings. A flat unramified morphism is called an étale morphism. Less strongly, if satisfies the conditions when restricted to sufficiently small neighborhoods of and , then is said to be unramified near . Some authors prefer to use weaker conditions, in which case they call a morphism satisfying the above a G-unramified morphism.

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