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Arithmetic bigness and a uniform Bogomolov-type result

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arxiv 2108.05625 v4 pith:KNG3MKEZ submitted 2021-08-12 math.NT math.AG

Xinyi Yuan This is my paper · ORCID
classification math.NTmath.AG
keywords uniformadelicbogomolov-typebundlecurveslineproveresult
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In this paper, we prove that the admissible canonical bundle of the universal family of curves is a big adelic line bundle, and apply it to prove a uniform Bogomolov-type theorem for curves over global fields of all characteristics. This gives a different approach to the uniform Mordell-Lang type of result of Dimitrov-Gao-Habegger and Kuhne. The treatment is based on the recent theory of adelic line bundles of Yuan-Zhang.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Non-Archimedean Rigidity and Uniformity for Common Preperiodic Points

    math.DS 2026-07 conditional novelty 8.0 of 10

    Any two complex polynomials either share all preperiodic points or have a uniformly bounded number of common preperiodic points, with the bound depending only on the degrees.

  2. Concave transforms of compactified S-metrized divisors

    math.AG 2025-05 conditional novelty 7.0 of 10

    For big compactified S-metrized divisors on quasi-projective varieties over adelic curves, concave transforms are constructed and shown to satisfy arithmetic volume and Hilbert-Samuel formulas.

  3. Deligne pairing for equidimensional morphisms

    math.AG 2024-11 conditional novelty 7.0 of 10

    For surjective projective morphisms of pure relative dimension d over normal schemes, this paper constructs a symmetric multi-additive Deligne pairing on d+1 line bundles, with functorial properties and canonical herm...

  4. Global pluripotential theory for adelic line bundles

    math.AG 2025-07 conditional novelty 6.0 of 10

    The category of strongly semiample adelic line bundles on a quasi-projective arithmetic variety is equivalent to line bundles on its Berkovich analytification with norm-equivariant continuous semipositive metrics.

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