Dynamical canonical heights for Jordan blocks, arithmetic degrees of orbits, and nef canonical heights on abelian varieties
نویسندگان
چکیده
منابع مشابه
Computing canonical heights using arithmetic intersection theory
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...
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 کاملCanonical Heights for Random Iterations in Certain Varieties
We show the existence of canonical heights (normalized heights) of subvarieties for bounded sequences of morphisms and give some applications.
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...
متن کاملLocal Heights on Abelian Varieties and Rigid Analytic Uniformization
We express classical and p-adic local height pairings on an abelian variety with split semistable reduction in terms of the corresponding pairings on the abelian part of the Raynaud extension (which has good reduction). Here we use an approach to height pairings via splittings of biextensions which is due to Mazur and Tate. We conclude with a formula comparing Schneider's p-adic height pairing ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2015
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/6596