BIRS Workshop Lecture Videos

Banff International Research Station Logo

BIRS Workshop Lecture Videos

Variation of the root number in families of elliptic curves Desjardins, Julie


What can we say about the variation of the rank in a family of elliptic curves We know in particular that if infinitely many curves in the family have non-zero rank, then the set of rational points is Zariski dense in the associated elliptic surface. We use a â conjectural substituteâ for the geometric rank (or rather for its parity) : the root number. For a non-isotrivial family, under two analytic number theory conjectures I show that the root number is -1 (resp. +1) for infinitely many curves in the family. On isotrivial families however, the root number may be constant : I describe its behaviour in this case.

Item Media

Item Citations and Data


Attribution-NonCommercial-NoDerivatives 4.0 International