In
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, more specifically in
algebra
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...
, the adjective étale refers to several closely related concepts:
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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 t ...
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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 ...
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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 conjectu ...
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Étale topology In mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. Th ...
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Étale fundamental group
The étale or algebraic fundamental group is an analogue in algebraic geometry, for schemes, of the usual fundamental group of topological spaces.
Topological analogue/informal discussion
In algebraic topology, the fundamental group \pi_1(X,x) o ...
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Étale group scheme In mathematics, more specifically in algebra
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic ...
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Étale algebra In commutative algebra, an étale algebra over a field (mathematics), field is a special type of algebra (ring theory), algebra, one that is isomorphism, isomorphic to a finite product of finite extension, finite separable field extensions. An éta ...
Other
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Étale (mountain)
Étale is a mountain of Savoie and Haute-Savoie, France
France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Sa ...
in Savoie and Haute-Savoie, France
See also
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Étalé space
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Etail, or online commerce
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