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An effective proof of the hyperelliptic Shafarevich conjecture

Rafael von Känel — 2014

Journal de Théorie des Nombres de Bordeaux

Let C be a hyperelliptic curve of genus g ≥ 1 over a number field K with good reduction outside a finite set of places S of K . We prove that C has a Weierstrass model over the ring of integers of K with height effectively bounded only in terms of g , S and K . In particular, we obtain that for any given number field K , finite set of places S of K and integer g ≥ 1 one can in principle determine the set of K -isomorphism classes of hyperelliptic curves over K of genus g with good reduction outside S .

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