Let $C_*$ be a chain complex of abelian groups.
Is it true that $H_i(C_*\otimes \mathbb{Z}/p)=0$ for all $i$ if and only if $H_i(C_*\otimes \mathbb{Z}_p)=0$ for all $i$, where $\mathbb{Z}_p$ is localization of $\mathbb{Z}$ away from $p$?
And I want to know that the precise definition of localization of $\mathbb{Z}$ away from $p$. Is it equal to $\mathbb{Z}[\frac{1}{p}]$ or $(\mathbb{Z}-p\mathbb{Z})^{-1}\mathbb{Z}$?