منابع مشابه
Canonical Heights and the Arithmetic Complexity of Morphisms on Projective Space
The theory of canonical heights on abelian varieties originated with the work of Néron [10] and Tate (first described in print by Manin [8]) in 1965. Tate’s simple and elegant limit construction uses a Cauchy sequence telescoping sum argument. Néron’s construction, which is via more delicate local tools, has proven to be fundamental for understanding the deeper properties of the canonical heigh...
متن کاملDynamics of Projective Morphisms Having Identical Canonical Heights
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...
متن کاملCanonical 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.
متن کاملHeights on the Finite Projective Line
Define the height function h(a) = min{k + (ka mod p) : k = 1, 2, . . . , p − 1} for a ∈ {0, 1, . . . , p − 1.} It is proved that the height has peaks at p, (p+1)/2, and (p+c)/3, that these peaks occur at a = [p/3], (p−3)/2, (p− 1)/2, [2p/3], p − 3, p− 2, and p − 1, and that h(a) ≤ p/3 for all other values of a. 1. Heights on finite projective spaces Let p be an odd prime and let Fp = Z/pZ and F...
متن کاملCanonical Heights on Genus Two Jacobians
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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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1997
ISSN: 0022-314X
DOI: 10.1006/jnth.1997.2099