20/05/04 16:48:52.52 ncpDqOGk.net
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URLﾘﾝｸ(ja.wikipedia.org)
エタール射
エタール射（エタールしゃ、etale morphism）とは、数学において有限型スキーム間の平坦かつ不分岐な射のこと。
目次
1 不分岐
2 平坦
3 同値な定義
4 類体論と不分岐の対応
URLﾘﾝｸ(en.wikipedia.org)
Etale morphism
In algebraic geometry, an etale morphism (French: [etal]) is a morphism of schemes that is formally etale and locally of finite presentation.
This is an algebraic analogue of the notion of a local isomorphism in the complex analytic topology.
They satisfy the hypotheses of the implicit function theorem, but because open sets in the Zariski topology are so large, they are not necessarily local isomorphisms.
Despite this, etale maps retain many of the properties of local analytic isomorphisms, and are useful in defining the algebraic fundamental group and the etale topology.
The word etale is a French adjective, which means "slack", as in "slack tide", or, figuratively, calm, immobile, something left to settle.[1]
Contents
1 Definition
2 Examples
3 Properties
4 Inverse function theorem