edoc

The intersection of a curve with a union of translated codimension-two subgroups in a power of an elliptic curve

Viada, Evelina. (2008) The intersection of a curve with a union of translated codimension-two subgroups in a power of an elliptic curve. Algebra and Number Theory, 2 (3). pp. 249-298.

[img] PDF - Published Version
Restricted to Repository staff only

1214Kb

Official URL: http://edoc.unibas.ch/dok/A5260089

Downloads: Statistics Overview

Abstract

Let E be an elliptic curve. An irreducible algebraic curve C embedded in a power A of E is called weak-transverse if it is not contained in any proper algebraic subgroup of A, and transverse if it is not contained in any translate of such a subgroup. Suppose E and C are defined over the algebraic numbers. First we prove that the algebraic points of a transverse curve C that are close to the union of all algebraic subgroups of E g of codimension 2 translated by points in a subgroup G of A of finite rank are a set of bounded height. The notion of closeness is defined using a height function. If G is trivial, it is sufficient to suppose that C is weak-transverse. The core of the article is the introduction of a method to determine the finite- ness of these sets. From a conjectural lower bound for the normalized height of a transverse curve C , we deduce that the sets above are finite. Such a lower bound exists for g ≤ 3. Concerning the codimension of the algebraic subgroups, our results are best possible.
Faculties and Departments:05 Faculty of Science
UniBasel Contributors:Viada, Evelina
Item Type:Article, refereed
Article Subtype:Research Article
Bibsysno:Link to catalogue
Publisher:Mathematical Sciences Publishers
ISSN:1937-0652
e-ISSN:1944-7833
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:15 Nov 2017 08:51
Deposited On:22 Mar 2012 13:51

Repository Staff Only: item control page