Algebraic Geometry Seminar
Salim Tayou
Darthmouth College
On the torsion locus of the Ceresa normal function
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.
Monday October 21, 2024 at 3:00 PM in 636 SEO