Reminder - ICTP Math Associates Seminar (Zoom Meeting) - Thursday 19 November at 14:00 (Cecília Salgado)

[ICTP Math Section]

Math Associates Seminar


Thursday 19 November 2020, at 14:00, Central European Time


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Speaker: Cecília Salgado (UFRJ)


Title: Mordell Weil rank jumps and the Hilbert property

Abstract: In this talk I will discuss recent progress around the 
variation of the Mordell-Weil rank in families of elliptic curves. The 
first part will be dedicated to give a thorough introduction to the 
theme, by motivating and discussing the state of the art. The second 
part will be dedicated to presenting a recent work joint with Dan 
Loughran (Bath). More precisely, let X be surface endowed with a 
(non-constant) elliptic fibration with a section defined over a number 
field. Specialization theorems by Néron and Silverman imply that the 
rank of the Mordell-Weil 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 larger than the latter. 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.