Abelian varieties are not quotients of low-dimension Jacobians

2023/02/12 by Jacob Tsimerman, Tsimerman, Jacob · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2302.05860

openalex publication_date 2023/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for any two integers g≥ 4 and g'≤ 2g-1, there exist abelian varieties over ℚ which are not quotients of a Jacobian of dimension g'. Our method in fact proves that most Abelian varieties satisfy this property, when counting by height relative to a fixed finite map to projective space.

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• Towards a p-adic nowhere density conjecture of Hecke Orbits

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