منابع مشابه
On metric heights
Metric heights are modified height functions on the non-zero algebraic numbers Q ∗ which can be used to define a metric on certain cosets of Q ∗ . They have been defined with a view to eventually applying geometric methods to the study of Q ∗ . In this paper we discuss the construction of metric heights in general. More specifically, we study in some detail the metric height obtained from the n...
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This expository article introduces some conjectures and theorems related to the Faltings heights of abelian varieties with complex multiplication. The topics include the Colmez conjecture, the averaged Colmez conjecture, and the André–Oort conjecture.
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 کاملPerpendicularity in an Abelian Group
We give a set of axioms to establish a perpendicularity relation in anAbelian group and then study the existence of perpendicularities in (Z n , +) and (Q + , ⋅) and in certain other groups. Our approach provides a justification for the use of the symbol⊥ denoting relative primeness in number theory and extends the domain of this convention to some degree. Related to that, we also consider para...
متن کاملOn the Subgroup Lattice of an Abelian Finite Group
The aim of this paper is to give some connections between the structure of an abelian finite group and the structure of its subgroup lattice. Let (G, +) be an abelian group. Then the set L(G) of subgroups of G is a modular and complete lattice. Moreover, we suppose that G is finite of order n. If L n is the divisors lattice of n, then the following function is well defined: ord : L(G) −→ L n , ...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2014
ISSN: 0035-7596
DOI: 10.1216/rmj-2014-44-6-2075