Rafael von Känel

collaborators

3 papers

math.NT2013

Szpiro's small points conjecture for cyclic covers

Ariyan Javanpeykar, Rafael von Känel

Let $X$ be a smooth, projective and geometrically connected curve of genus at least two, defined over a number field. In 1984, Szpiro conjectured that $X$ has a "small point". In t…

math.NT2013

On Szpiro's Discriminant Conjecture

Rafael von Känel

We consider generalizations of Szpiro's classical discriminant conjecture to hyperelliptic curves over a number field $K$ , and to smooth, projective and geometrically connected cur…

math.NT2013

An effective proof of the hyperelliptic Shafarevich conjecture

Rafael von Känel

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…