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In mathematics, more specifically in
algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...
, the adjective étale refers to several closely related concepts: *
Étale morphism In algebraic geometry, an étale morphism () is a morphism of schemes that is formally étale and locally of finite presentation. This is an algebraic analogue of the notion of a local isomorphism in the complex analytic topology. They satisfy th ...
**
Formally étale morphism In commutative algebra and algebraic geometry, a morphism is called formally étale if it has a lifting property that is analogous to being a local diffeomorphism. Formally étale homomorphisms of rings Let ''A'' be a topological ring, and let ...
*
Étale cohomology In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil conjecture ...
*
Étale topology In algebraic geometry, the étale topology is a Grothendieck topology on the category of schemes which has properties similar to the Euclidean topology, but unlike the Euclidean topology, it is also defined in positive characteristic. The étale t ...
* Étale fundamental group * Étale group scheme * Étale algebra


Other

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Étale (mountain) Étale is a mountain of Savoie and Haute-Savoie, France. It lies in the Aravis Range The Aravis (french: Chaîne des Aravis) is a mountain range in Savoie and Haute-Savoie, eastern France. It is part of the French Prealps, a lower chain of mounta ...
in Savoie and Haute-Savoie, France


See also

* Étalé space *
Etail Online shopping is a form of electronic commerce which allows consumers to directly buy goods or services from a seller over the Internet using a web browser or a mobile app. Consumers find a product of interest by visiting the website of the ...
, or online commerce {{disambig