Étale Cohomology

A sheaf cohomology theory on the étale site of a scheme that assigns cohomological invariants to schemes and varieties, bridging algebraic geometry, arithmetic and analogues of topological cohomology (e.g., l-adic cohomology and comparison theorems).

A sheaf cohomology theory computed on the étale site of a scheme, producing groups H^i_et(X, F) for étale sheaves F (and their l-adic completions) that reflect arithmetic and geometric information, and carry Galois actions for varieties over non algebraically closed fields.