Constant root number on integer fibres of elliptic surfaces

Abstract: In this joint work with Julie Desjardins, we aim to describe all non-isotrivial families of elliptic curves with low-degree coefficients such that the root number is constant for every integer fibre in the family. We motivate this talk by studying properties of the root number in families of elliptic curves and Washington's example $\mathcal{W}_t: y^2=x^3+tx^2-(t+3)x+1$ for which Rizzo showed has constant root number -1 for all $t \in \mathbb{Z}$.

algebraic geometrycombinatoricsdynamical systemsgeneral topologynumber theory

Audience: researchers in the topic

ZORP (zoom on rational points)

Series comments: 2 talks on a Friday, roughly once per month.

Online coffee break in between.