# Homological and homotopical equivalence of complex analytic varieties

Consider a map between two complex analytic varieties of finite type $$f:X\to Y$$. Suppose that $$f$$ induces isomorphisms on cohomology with (constant) integral coefficients. Under what reasonable hypotheses can we conclude that it induces an equivalence on homotopy groups?

I refer in particular to this article https://arxiv.org/pdf/1710.05366.pdf, Proof of proposition 3.17 on page 14, where the Authors use a result of this kind. I cannot understand why classical hypotheses like nilpotency of the spaces are verified.