Church-Turing computability of the étale cohomology mod l

[Work in common with Fabrice Orgogozo]The dimension of the étale cohomology groups, with coefficients in Z/lZ, of a scheme of finite type over an algebraically closed field of characteristic different from l, is computable in the sense of Church-Turing. To prove this, we construct a hypercovering of X by schemes (analogous to Artin’s ?Roegood neighborhoods?R) having algorithmically testable geometric properties which allow to reduce the computation of the cohomology of X to that of their completed fundamental group.