Valuations, intersections and Belyi functions--some remarks on the construction of heights

DOI10.1016/j.exmath.2006.06.002zbMath1142.14014OpenAlexW2110739557MaRDI QIDQ996991

Răzvan Liţcanu

Publication date: 19 July 2007

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.exmath.2006.06.002

zbMATH Keywords

Bogomolov conjectureBelyĭ mapNéron-Tate canonical height

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Coverings of curves, fundamental group (14H30) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Cites Work

• Admissible pairing on a curve
• Characteristic classes for algebraic vector bundles with Hermitian metric. I
• Calculus on arithmetic surfaces
• Diophantine approximation on abelian varieties
• Arithmetic characteristic classes of automorphic vector bundles
• Métriques sur les fibrés d'intersection. (Metrics on intersection fiber bundles)
• Equidistribution of small points on abelian varieties
• Positivity and discretion of algebraic points of curves
• Arithmetic intersection theory
• Sur des hauteurs alternatives. II (On alternative heights. II)
• Equidistribution of small points
• Properties of the degree of Belyi functions. (Proprieétés du degré des morphismes de Belyi.)
• Algebraic independence criteria.
• An effective version of Belyi's theorem.
• Arithmetic Hilbert-Samuel theorem
• Positive line bundles on arithmetic surfaces
• An arithmetic Riemann-Roch theorem
• Quasi-functions and heights on abelian varieties
• Coverings of Algebraic Curves
• COHOMOLOGICAL ARITHMETIC CHOW RINGS
• Heights and Arakelov's Intersection Theory
• On Second Order Linear Differential Equations with Algebraic Solutions
• Heights in number fields
• ON GALOIS EXTENSIONS OF A MAXIMAL CYCLOTOMIC FIELD
• INTERSECTION THEORY OF DIVISORS ON AN ARITHMETIC SURFACE
• Heights of Projective Varieties and Positive Green Forms
• Current Trends in Arithmetical Algebraic Geometry
• Positive Line Bundles on Arithmetic Varieties
• Arithmetic on algebraic varieties
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