Title	Variation of the root number in families of elliptic curves
Creator	Desjardins, Julie
Publisher	Banff International Research Station for Mathematical Innovation and Discovery
Date Issued	2018-05-28T15:23
Description	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.
Extent	36.0
Subject	Mathematics; Number theory; Algebraic geometry; Arithmetic number theory
Type	Moving Image
File Format	video/mp4
Language	eng
Notes	Author affiliation: Max Planck Institute for Mathematics
Series	BIRS Workshop Lecture Videos (Oaxaca de Juárez (Mexico))
Date Available	2019-03-14
Provider	Vancouver : University of British Columbia Library
Rights	Attribution-NonCommercial-NoDerivatives 4.0 International
DOI	10.14288/1.0376859
URI	http://hdl.handle.net/2429/68693
Affiliation	Non UBC
Peer Review Status	Unreviewed
Scholarly Level	Postdoctoral
Rights URI	http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository	DSpace

Open Collections

BIRS Workshop Lecture Videos