Morphisms inverted by profinite completion (Q1116493)

The author shows that a map between nilpotent spaces becomes an equivalence upon P-profinite completion, where P is a collection of primes, if and only if it is an equivalence with respect to mod p homology for all p in P. Homological criteria for a homomorphism between nilpotent groups to become an isomorphism or an epimorphism under P- profinite completion are given. These results are relativised to nilpotent fibrations and relative groups.