{"id":"hexagon/2610.00413","pdf":"https://hexagonmath.org/pdf/2610.00413v2","url":"https://hexagonmath.org/abs/2610.00413v2","tags":["math.NT","msc:14C25","msc:14G35","msc:11G18"],"score":0,"title":"Testing the non-vanishing of the Ceresa cycle of $X_0(N)$","domain":"math.AG","source":"hexagon","authors":["Leonardo Finzi"],"reviews":0,"subject":"math.AG","summary":"For a curve $C$ and a fixed degree-one divisor $e$ of $C$, we can embed $C$ into its Jacobian. This embedding induces an algebraic $1$-cycle on the Jacobian called the Ceresa cycle, which we denote by $\\mathrm{Cer}(C,e)$. Although homologically trivial, Ceresa cycles of very general curves with genus $\\geq 3$ are non-trivial under algebraic equivalence. It is generally unknown whether a very general curve admits a non-trivial Ceresa cycle modulo rational equivalence. In this paper, we explore the non-triviality under rational equivalence of the Ceresa cycle corresponding to the modular curve…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Magma"],"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}