Salim Tayou : On the torsion locus of the Ceresa normal function

Posted by Philip Engel , part of the Algebraic Geometry Seminar.

At

Oct. 21, 2024, 3 p.m.

In

636 SEO

Abstract

The Ceresa cycle is a homologically trivial cycle that lives on the Jacobian of any smooth proper curve of genus g. Its image under the Abel-Jacobi map defines a normal function on M_g and Ceresa famously proved that this normal function is generically non-torsion. In this talk, I will explain a joint recent work with Matt Kerr where we prove that the positive-dimensional part of the torsion locus of the Ceresa normal function in M_g is not Zariski dense when g>2. Moreover, it has only finitely many components with generic Mumford-Tate group equal to GSp_2g, these components are defined over the algebraic closure of Q and their union is closed under the action of the absolute Galois group of Q. This result follow from a general study of the distribution of the torsion locus of arbitrary admissible normal functions.