منابع مشابه
Canonical Heights on Hyperelliptic Curves
We describe an algorithm to compute canonical heights of points on hyperelliptic curves over number fields, using Arakelov geometry. We include a worked example for illustration purposes.
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Let K be a number field and let C/K be a curve of genus 2 with Jacobian variety J . In this paper, we study the canonical height ĥ : J(K) → R. More specifically, we consider the following two problems, which are important in applications: (1) for a given P ∈ J(K), compute ĥ(P ) efficiently; (2) for a given bound B > 0, find all P ∈ J(K) with ĥ(P ) ≤ B. We develop an algorithm running in polynom...
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The canonical height ĥ on an abelian variety A defined over a global field k is an object of fundamental importance in the study of the arithmetic of A. For many applications it is required to compute ĥ(P ) for a given point P ∈ A(k). For instance, given generators of a subgroup of the Mordell-Weil group A(k) of finite index, this is necessary for most known approaches to the computation of gen...
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Let φ,ψ : PN → PN be morphisms of degree at least 2 whose canonical heights ĥφ and ĥψ are identical. We draw various conclusions about the Green functions, Julia sets, and canonical local heights of φ and ψ. We use this information to completely characterize φ and ψ in the following cases: (i) φ and ψ are polynomial maps in one variable; (ii) φ is the dth-power map; (iii) φ is a Lattès map. Int...
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We show the existence of canonical heights (normalized heights) of subvarieties for bounded sequences of morphisms and give some applications.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2019
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2019.02.020