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Adelic line bundles on quasi-projective varieties

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arxiv 2105.13587 v9 pith:II2PKJX5 submitted 2021-05-28 math.NT math.AG

Xinyi Yuan , Shou-Wu Zhang This is my paper · ORCID
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keywords theoryadelicbundleslinequasi-projectivevarietiesalgebraicapply
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In this book, we establish a theory of adelic line bundles over quasi-projective varieties over finitely generated fields. Besides definitions of adelic line bundles, we consider their intersection theory, volume theory, and height theory, and apply these to study heights of algebraic points of quasi-projective varieties.

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Cited by 3 Pith papers

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

  1. 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.

  2. Equidistribution for semiabelian varieties over number fields

    math.NT 2026-08 conditional novelty 6.0 of 10

    For monocritical arithmetically T-effective toric metrics on semiabelian compactifications, generic small sequences equidistribute and minimal-height subvarieties are special.

  3. 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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