I have a question about an argument in a proof from Bosch's "Neron Models" (page 47):
It's not clear to me how to see that (d) implies (e).
According to the author's sketch it's a consequence of Thm. 2, namely the ZMT:
Here I see following problem: to avoid the separateness problem we observe that this is a local problem therefore we can take an open affine set $U= Spec(A)$ containing $x$ and apply $ZMT$ to the compostion $U \to X \to S$. Where do we here really need the condition (d)?