Étale
Encyclopedia
In mathematics
, more specifically in algebra
, the adjective étale refers to several closely related concepts:
Other:
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, more specifically in algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
, the adjective étale refers to several closely related concepts:
- Étale morphismÉtale morphismIn algebraic geometry, a field of mathematics, an étale morphism 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...
- Formally étale morphismFormally étale morphismIn commutative algebra and algebraic geometry, a morphism is called formally étale if has a lifting property that is analogous to being a local diffeomorphism.- Formally étale homomorphisms of rings :...
- Formally étale morphism
- Étale cohomologyÉtale cohomologyIn 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 conjectures...
- Étale topologyÉtale topologyIn 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...
- Étale fundamental groupÉtale fundamental groupThe étale fundamental group is an analogue in algebraic geometry, for schemes, of the usual fundamental group of topological spaces.-Topological analogue:In algebraic topology, the fundamental group\pi_1...
- Étale space
- Étale group scheme
- Étale algebra
Other:
- ÉtaleÉtale (mountain)Étale is a mountain of Savoie and Haute-Savoie, France. It lies in the Aravis range. It has an altitude of 2484 metres above sea level....
is a mountain of SavoieSavoieSavoie is a French department located in the Rhône-Alpes region in the French Alps.Together with the Haute-Savoie, Savoie is one of the two departments of the historic region of Savoy that was annexed by France on June 14, 1860, following the signature of the Treaty of Turin on March 24, 1860...
and Haute-SavoieHaute-SavoieHaute-Savoie is a French department in the Rhône-Alpes region of eastern France. It borders both Switzerland and Italy. The capital is Annecy. To the north is Lake Geneva and Switzerland; to the south and southeast are the Mont Blanc and Aravis mountain ranges and the French entrance to the Mont...
in France.