# Etale-analytic comparison without elementary fibrations

A theorem due to Artin says that for a smooth scheme $$X$$ of finite type on $$mathbb {C}$$ and a locally consistent buildable sheaf $$F$$ we have an isomorphism
$$H ^ * _ {and} (X, F) approximately H ^ * (X ( mathbb {C}), F)$$
where the LHS is the étale cohomology and the RHS is the cohomology of the functors derived from $$F$$ in analytical topology. One of the proofs I know is that there is open coverage of $$X$$ by $$K ( pi, 1)$$ the spaces. However, the appearance of $$K ( pi, 1)$$feels a little odd to me. Is there any alternative proof that does not rely on $$K ( pi, 1)$$ neighborhoods?