Séminaires : Séminaire Théorie des Nombres

Equipe(s) : tn,
Responsables :Ziyang Gao, Marc Hindry, Bruno Kahn, João Pedro P. dos Santos
Email des responsables : ziyang.gao@imj-prg.fr
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Description

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Orateur(s) Abbey Bourdon - Wake Forest University,
Titre On Isolated Points of Odd Degree
Date28/09/2020
Horaire14:00 à 15:00
Diffusion https://bigbluebutton2.imj-prg.fr/b/joa-4zg-7rk
RésumeLet C be a curve defined over a number field k. We say a closed point x on C of degree d is isolated if it does not belong to an infinite family of degree d points parametrized by the projective line or a positive rank abelian subvariety of the curve's Jacobian. There are only finitely many isolated points on C of any degree, and this collection can be difficult to identify explicitly, especially as the genus of C (and thus the possible degree of an isolated point) grows. Motivated by the well-known problem of classifying torsion subgroups of elliptic curves over number fields, we will restrict to the case where C is the modular curve X_1(N). Prior joint work with Ejder, Liu, Odumodu, and Viray showed that there are only finitely many elliptic curves with rational j-invariant which give rise to an isolated point of any degree on any modular curve of the form X_1(N), assuming Serre's Uniformity Conjecture. In this talk, I will discuss a recent unconditional version of this result for isolated points of odd degree, which is joint work with David Gill, Jeremy Rouse, and Lori Watson.
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AdresseBigBlueButton TN
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