Siegel’s theorem and the Shafarevich conjecture
Aaron Levin (2012)
Journal de Théorie des Nombres de Bordeaux
Similarity:
It is known that in the case of hyperelliptic curves the Shafarevich conjecture can be made effective, i.e., for any number field and any finite set of places of , one can effectively compute the set of isomorphism classes of hyperelliptic curves over with good reduction outside . We show here that an extension of this result to an effective Shafarevich conjecture for of hyperelliptic curves of genus would imply an effective version of Siegel’s theorem for integral points...