%0 Journal Article
%T Siegel's Theorem and the Shafarevich Conjecture
%A Aaron Levin
%J Mathematics
%D 2011
%I arXiv
%X It is known that in the case of hyperelliptic curves the Shafarevich conjecture can be made effective, i.e., for any number field k and any finite set of places S of k, one can effectively compute the set of isomorphism classes of hyperelliptic curves over k with good reduction outside S. We show here that an extension of this result to an effective Shafarevich conjecture for Jacobians of hyperelliptic curves of genus g would imply an effective version of Siegel's theorem for integral points on hyperelliptic curves of genus g.
%U http://arxiv.org/abs/1109.6070v2