## Etale-analytic comparison without elementary fibrations.

A theorem due to Artin states that for a smooth scheme $$X$$ of finite type about $$mathbb {C}$$ and a constant locally constructible sheaf $$F$$ we have an isomorphism
$$H ^ * et (X, F) approx H ^ * (X ( mathbb {C}), F)$$
where the LHS is ethnic cohomology and the RHS is cohomology functor derived from $$F$$ In the analytical topology. One of the tests that I know comes from establishing that there is an open cover of $$X$$ by $$K ( pi, 1)$$ However, the appearance of $$K ( pi, 1)$$I feel a little weird. Is there any alternative test that is not based on $$K ( pi, 1)$$ neighborhoods