TITLE: Does the Mordell conjecture imply the Shafarevich conjecture
QUESTION [5 upvotes]: The base field is a number field.
It is known that the Shafarevich conjecture implies the Mordell conjecture (Kodaira-Parshin).
Is the converse also true? 
Note that both conjectures are now theorems (Faltings).
Edit: To be clear, I'm referring to the Shafarevich conjecture for curves. That is, for any number field $K$, finite set of places $S$ of $K$ and integer $g > 1$, the set of curves over $K$ of genus $g$ with good reduction outside $S$ is finite.

REPLY [6 votes]: The Shafarevich conjecture can be interpreted as stating that the set of $S$-integral points (over any number field) on the moduli space of curves of fixed genus (or principally polarized abelian varieties of fixed dimension) is finite. So, in this sense, it is a generalization of Siegel's theorem/Mordell's conjecture. But note that it is a statement about a variety of high dimension, so I very much doubt that you can reduce the Shafarevich conjecture to the Mordell conjecture. Except, of course, in the case of elliptic curves, where the Shafarevich conjecture follows directly from Siegel's theorem as Shafarevich originally remarked.