= Étale cohomology
{title2=$H^i_{\mathrm{et}}(X,\mathcal F)$}
{wiki}
Étale cohomology is <sheaf cohomology> on the site whose objects are <étale morphisms> $Y\to X$ and whose coverings are jointly surjective families of such morphisms. It provides cohomological invariants for <algebraic varieties> over fields of positive characteristic. In <Deligne-Lusztig theory>, compactly supported groups with $\ell$-adic coefficients, for $\ell$ different from the field characteristic, give finite-dimensional representations of the finite groups acting on the varieties.
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