2024/12/02 by Jordan S. Ellenberg, Adam Logan, Ellenberg, Jordan +2
Computer Science · Engineering · #14C25 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2412.02015
openalex publication_date 2024/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Ceresa cycle is a canonical algebraic 1-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 \operatorname*GSp, we prove that if the Ceresa class (the image of the Ceresa cycle in étale cohomology) is non-torsion, then the algorithm will eventually terminate with a certificate attesting to this fact.