**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 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.

Read more about Étale Cohomology: History, Motivation, Definitions, ℓ-adic Cohomology Groups, Properties, Calculation of étale Cohomology Groups, Examples of étale Cohomology Groups, Poincaré Duality and Cohomology With Compact Support, An Application To Curves