D\'ecompositions en hauteurs locales
Fabien Pazuki
TL;DR
This paper presents a decomposition formula for heights on Jacobian varieties of hyperelliptic curves over number fields, linking Faltings and Néron-Tate heights, and explores a Bogomolov-type question in the moduli space.
Contribution
It introduces a new decomposition formula for heights on Jacobians and formulates a Bogomolov-type conjecture for principally polarized abelian varieties.
Findings
Decomposition formula for Faltings height of Jacobians
Decomposition formula for Néron-Tate height of rational points
Formulation of a Bogomolov-type question in moduli space
Abstract
Let A be the jacobian variety of a hyperelliptic curve defined over a number field k. We provide a decomposition formula for the Faltings height of A and for the N\'eron-Tate height of k-rational points on A. We formulate a question of Bogomolov type on the space of principally polarized abelian varieties of dimension g.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Meromorphic and Entire Functions