On Certain Uniformity Properties of Curves Over Function Fields

Lucia Caporaso

doi:10.1023/A:1013703430436

Abstract

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A uniform version of the Shafarevich Conjecture for function fields (Theorem of Parshin–Arakelov) is proved, together with a uniform version of the geometric Mordell conjecture (Theorem of Manin). Such results are generalized to base varieties of arbitrary dimension (i.e. function fields of arbitrary transcendence degree).

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Caporaso, Lucia 2003. Remarks about uniform boundedness of rational points over function fields. Transactions of the American Mathematical Society, Vol. 355, Issue. 9, p. 3475.

Heier, Gordon 2004. Uniformly effective Shafarevich Conjecture on families of hyperbolic curves over a curve with prescribed degeneracy locus. Journal de Mathématiques Pures et Appliquées, Vol. 83, Issue. 7, p. 845.

Viehweg, Eckart 2010. Compactifications of smooth families and of moduli spaces of polarized manifolds. Annals of Mathematics, Vol. 172, Issue. 2, p. 809.

Kovács, Sándor and Lieblich, Max 2011. Erratum for Boundedness of families of canonically polarized manifolds: A higher dimensional analogue of Shafarevich's conjecture$^\ast$. Annals of Mathematics, Vol. 173, Issue. 1, p. 585.

Narkiewicz, Władysław 2012. Rational Number Theory in the 20th Century. p. 369.

Delzant, Thomas 2016. Kähler groups, $${\mathbb{R}}$$ R -trees, and holomorphic families of riemann surfaces. Geometric and Functional Analysis, Vol. 26, Issue. 1, p. 160.

Liu, Xiao-Lei and Tan, Sheng-Li 2017. Uniform bound for the effective Bogomolov conjecture. Comptes Rendus. Mathématique, Vol. 355, Issue. 2, p. 205.

Jöricke, Burglind 2022. Riemann surfaces of second kind and effective finiteness theorems. Mathematische Zeitschrift, Vol. 302, Issue. 1, p. 73.

Phung, Xuan Kien 2023. On the Parshin–Arakelov theorem and integral sections on elliptic surfaces. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 64, Issue. 2, p. 387.

Phung, Xuan Kien 2023. Finiteness criteria and uniformity of integral sections in some families of abelian varieties. Geometriae Dedicata, Vol. 217, Issue. 3,

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On Certain Uniformity Properties of Curves Over Function Fields

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

On Certain Uniformity Properties of Curves Over Function Fields

Abstract

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