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.
Thank you in advance.
EDIT: Posted in MO as https://mathoverflow.net/questions/354801/homological-and-homotopical-equivalence-of-complex-analytic-varieties