# Number Theory Seminar

Speaker: Richard Griffon (Basel)

Title: Isogenies of elliptic curves over function fields

Abstract: I will report on a  recently-completed project with Fabien Pazuki about elliptic curves over function fields and isogenies between them. In this work, we prove analogues in the function field setting of two famous theorems concerning isogenous elliptic curves over number fields. The first of these describes the variation of the Weil height of the j-invariant of an elliptic curve in an isogeny class. Our second main result is an isogeny estimate’’ in the spirit of theorems by Masser—Wüstholz and by Gaudron—Rémond. During the talk, I will state our results, sketch their proof and, time permitting, mention a few Diophantine applications thereof. I will also try to highlight similarities and differences between the number field and the function field cases.