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Currently displaying 1 – 2 of 2

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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 $g \geq 1$ 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 $g \geq 1$ one can in principle determine the set of $K$ -isomorphism classes of hyperelliptic curves over $K$ of genus $g$ with good reduction outside $S$ .

An effective Shafarevich theorem for elliptic curves

Clemens Fuchs; Rafael von Känel; Gisbert Wüstholz — 2011

Acta Arithmetica

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