4 papers
Variation of height in an isogeny class over a function field
Richard Griffon, Samuel Le Fourn, Fabien Pazuki
We give optimal estimates on the variation of the differential and modular heights within an isogeny class of abelian varieties defined over the function field of a curve (in any c…
Explicit height estimates for CM curves of genus 2
Linda Frey, Samuel Le Fourn, Elisa Lorenzo García
In this paper we make explicit the constants of Habegger and Pazuki's work from 2017 on bounding the discriminant of cyclic Galois CM fields corresponding to genus 2 curves with CM…
Bounding integral points on the Siegel modular variety A_2(2)
Josha Box, Samuel le Fourn
We determine two explicit upper bounds for the stable Faltings height of principally polarised abelian surfaces over number fields corresponding to S-integral points on the Siegel…
Quadratic Chabauty for modular curves and modular forms of rank one
Netan Dogra, Samuel Le Fourn
In this paper, we provide refined sufficient conditions for the quadratic Chabauty method to produce a finite set of points, with the conditions on the rank of the Jacobian replace…