Exercise 27, § 4

Give an example of a local homomorphism $\rho : A \to B$ and an $A$-module $M$ (not finitely generated) such that $\operatorname{Supp}(M_{(B)})$ is not equal to ${}^a\rho^{-1}(\operatorname{Supp}(M))$ (take $A = \mathbf{Z}_{(p)}$ and $B = \mathbf{Z}/p\mathbf{Z}$ for some prime number $p$).