Adelic line bundles on quasi-projective varieties

Abstract

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.

References in corpus (7)

• Formes différentielles réelles et courants sur les espaces de Berkovich
• Equidistribution of Dynamically Small Subvarieties over the Function Field of a Curve
• Equidistribution in Families of Abelian Varieties and Uniformity
• The Geometric Dynamical Northcott and Bogomolov Properties
• Effective bound of linear series on arithmetic surfaces
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Cited by in corpus (5)

• Equidistribution in Families of Abelian Varieties and Uniformity
• Recent developments of the Uniform Mordell-Lang Conjecture
• The Uniform Mordell-Lang Conjecture
• Arithmetic bigness and a uniform Bogomolov-type result
• Specialization of canonical heights on abelian varieties