On a question of Ekedahl and Serre

2017/03/30 by Ke Chen, Xin Lü, Chen, Ke +3
Mathematics · #14G40 #14H42 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1703.10377

openalex publication_date 2017/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study various aspects of the Ekedahl-Serre problem. We formulate questions of Ekedahl-Serre type and Coleman-Oort type for general weakly special subvarieties in the Siegel moduli space, propose a conjecture relating these two questions, and provide examples supporting these questions. The main new result is an upper bound of genera for curves over number fields whose Jacobians are isogeneous to products of elliptic curves satisfying the Sato-Tate equidistribution, and we also refine previous results showing that certain weakly special subvarieties only meet the open Torelli locus in at most finitely many points.

Citations

• A proof of the Andre-Oort conjecture for A_g
• Good Reduction of Abelian Varieties
• The Oort conjecture on Shimura curves in the Torelli locus of curves
• On Higgs bundles over Shimura varieties of ball quotient type
• Height pairings on orthogonal Shimura varieties

Related

• Spanning the isogeny class of a power of an ordinary elliptic curve over a finite field. Application to the number of rational points of curves of genus ≤ 4
• The Oort conjecture on Shimura curves in the Torelli locus of curves
• Serre's Uniformity Conjecture for Elliptic Curves with Rational Cyclic\n Isogenies
• The Oort conjecture for Shimura curves of small unitary rank
• An Improved Bound Towards a Conjecture of Serre on Surjective Galois Representations