Detection of integral acyclicity modulo primes
= Detection of integral acyclicity modulo primes
If a chain complex of finitely generated free abelian groups has zero homology after tensoring with $\mathbb F_p$ for every prime $p$, then its integral homology vanishes. The <universal coefficient theorem for homology> detects a free summand modulo every prime and detects a nonzero finite summand modulo any prime dividing its order.