Orateur(s)  Cecilia Salgado  Federal University of Rio de Janeiro and MPIM,

Titre  MordellWeil rank jumps and the Hilbert property 
Date  21/10/2019 
Horaire  14:00 à 15:00 

Résume  Let X be an elliptic surface with a section defined over a number field. Specialization theorems by Néron and Silverman imply that the rank of the MordellWeil group of special fibers is at least equal to the MW rank of the generic fiber. We say that the rank jumps when the former is strictly large than the latter. In this talk, I will discuss rank jumps for elliptic surfaces fibred over the projective line. If the surface admits a conic bundle we show that the subset of the line for which the rank jumps is not thin in the sense of Serre. This is joint work with Dan Loughran. 
Salle  salle 502, couloir 1525, Jussieu 
Adresse  Campus Pierre et Marie Curie
