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On a question of Ekedahl and Serre

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arxiv 1703.10377 v2 pith:7X4GTYHH submitted 2017-03-30 math.AG

Ke Chen , Xin Lu , Kang Zuo This is my paper · ORCID
classification math.AG
keywords questionscurvesekedahl-serrespecialsubvarietiestypeweaklyaspects
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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.

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  1. What makes an algebraic curve special?

    math.AG 2025-02 conditional novelty 3.0 of 10

    A survey of special curves and special subvarieties of moduli space, unifying Hodge-theoretic, Teichmüller, and bi-algebraic perspectives, with a few new results and conjectures.

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