e/Etale cohomology

Information
has gloss	eng: 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 conjectures. Étale cohomology theory can be used to construct ℓ-adic cohomology, which is an example of a Weil cohomology theory in algebraic geometry. This has many applications, such as the proof of the Weil conjectures and the construction of representations of finite groups of Lie type. History Étale cohomology was suggested by , using some suggestions by J.-P. Serre, and was motivated by the attempt to construct a Weil cohomology theory in order to prove the Weil conjectures. The foundations were soon after worked out by Grothendieck together with Michael Artin, and published as and SGA 4. Grothendieck used étale cohomology to prove some of the Weil conjectures (Dwork had already managed to prove the rationality part of the conjectures in 1960 using p-adic methods), and the remaining conjecture, the analogue of the Riemann hypothesis was proved by Pierre Deligne (1974) using ℓ-adic cohomology.
lexicalization	eng: Etale cohomology
lexicalization	eng: étale cohomology
lexicalization	eng: Étalé cohomology
instance of	c/Cohomology theories

Meaning
Japanese
has gloss	jpn: エタール・コホモロジー(étale cohomology)はアレクサンドル・グロタンディークがヴュイユ予想を証明するための道具として考案したコホモロジー理論であり、位相空間上の定数係数コホモロジー、すなわち特異コホモロジーの類似になっている。エタール・コホモロジーはヴュイユ・コホモロジーの一種であるℓ進コホモロジーを構成する枠組みを与える。代数幾何学における基本的な道具の一つで、非常に多くの応用を持ち、ヴュイユ予想への貢献やフェルマーの最終定理の証明の際にも用いられた。
lexicalization	jpn: エタール・コホモロジー
Portuguese
has gloss	por: Em matemática, a cohomologia etal de grupos de uma variedade algébrica ou esquema são análogos algébricos da usual cohomologia de grupos com finitos coeficientes de um espaço topológico, introduzido por Grothendieck de maneira a provar as conjecturas de Weil. A teoria da cohomologia etal pode ser usada para construir chomologia l-ádica, a qual é um exemplo de uma teoria da cohomologia de Weil em geometria algébrica. Isto tem muitas aplicações, tais como a demonstração das conjecturas de Weil e a construção de conjectures and the construction of representações de grupos finitos do tipo Lie.
lexicalization	por: Cohomologia etal