Étale cohomology

Summary

Étale cohomology is a cohomology theory for schemes, built from sheaves on the étale site instead of the Zariski topology. Grothendieck and Artin introduced it to obtain, for varieties over any field, groups that behave like the singular cohomology of a complex variety. It contains Galois cohomology as the case of a point. It is the setting of ℓ-adic cohomology and of Deligne's proof of the Weil conjectures.