Certifying nontriviality of Ceresa classes of curves
Jordan Ellenberg, Adam Logan, Padmavathi Srinivasan

TL;DR
This paper develops an algorithm to certify the non-torsion property of Ceresa classes of algebraic curves over number fields, providing a practical tool for understanding their algebraic cycles without symmetry assumptions.
Contribution
It introduces a new algorithm for certifying non-torsion of Ceresa classes and proves its correctness under the full Sato--Tate group hypothesis.
Findings
Algorithm often certifies non-torsion of Ceresa classes.
Under Sato--Tate group assumptions, the algorithm terminates with a certificate.
Provides a method to verify nontriviality of Ceresa classes without extra symmetries.
Abstract
The Ceresa cycle is a canonical algebraic -cycle on the Jacobian of an algebraic curve. We construct an algorithm which, given a curve over a number field, often provides a certificate that the Ceresa cycle is non-torsion, without relying on the presence of any additional symmetries of the curve. Under the hypothesis that the Sato--Tate group is the whole of , we prove that if the Ceresa class (the image of the Ceresa cycle in \'{e}tale cohomology) is non-torsion, then the algorithm will eventually terminate with a certificate attesting to this fact.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Polynomial and algebraic computation
