Heights of points with bounded ramification

Pottmeyer, Lukas. (2015) Heights of points with bounded ramification. Annali della Scuola Normale di Pisa - Classe di Scienze, 14 (3). pp. 965-981.

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Let E be an elliptic curve defined over a number field K with fixed non-archimedean absolute value v of split-multiplicative reduction, and let f be an associated Lattes map. Baker proved in [3] that the Neron-Tate height on E is either zero or bounded from below by a positive constant, for all points of bounded ramification over v. In this paper we make this bound effective and prove an analogue result for the canonical height associated to f. We also study variations of this result by changing the reduction type of E at v. This will lead to examples of fields F such that the Neron-Tate height on non-torsion points in E (F) is bounded from below by a positive constant and the height associated to f gets arbitrarily small on F.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Zahlentheorie (Habegger)
UniBasel Contributors:Pottmeyer, Lukas
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Scuola Normale Superiore, Pisa
Note:Publication type according to Uni Basel Research Database: Journal article
Identification Number:
Last Modified:22 Nov 2016 12:58
Deposited On:17 May 2016 09:24

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