Glossary of Arithmetic and Diophantine Geometry - E

E

Étale cohomology

The search for a Weil cohomology (q.v.) was at least partially fulfilled in the étale cohomology theory of Alexander Grothendieck and Michael Artin. It provided a proof of the functional equation for the local zeta-functions, and was basic in the formulation of the Tate conjecture (q.v.) and numerous other theories.