Weakly bounded height on modular curves

Habegger, Philipp. (2010) Weakly bounded height on modular curves. Acta Mathematica Vietnamica, 35 (1). pp. 43-69.

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We study the intersection of a fixed plane algebraic curve C with modular curves of varying level. The height of points in such intersections cannot be bounded from above independently of the level when C is defined over the field of algebraic numbers. But we find a certain class of curves C for which the height is bounded logarithmically in the level. This bound is strong enough to imply certain finiteness result. Such evidence leads to a conjecture involving a logarithmic height bound unless C is of so-called special type. We also discuss connections to recent progress on conjectures concerning unlikely intersections.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Zahlentheorie (Habegger)
UniBasel Contributors:Habegger, Philipp
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Institute of Mathematics
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:15 Jan 2018 09:01
Deposited On:15 Jan 2018 09:01

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