Siegel's Theorem and the Shafarevich Conjecture

Details Siegel's Theorem and the Shafarevich Conjecture Siegel's Theorem and the Shafarevich Conjecture

2011-09-28

arxiv.org/abs/1109.6070v2

Mathematics

Number Theory

Updated comments and attributions concerning Theorem 4

Scientific paper

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.

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