The Tate-Voloch conjecture in a power of a modular curve

Habegger, Philipp. (2014) The Tate-Voloch conjecture in a power of a modular curve. International Mathematics Research Notices, 2014 (12). pp. 3303-3339.

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Let p be a prime. Tate and Voloch proved that a point of finite order in the algebraic torus cannot be p-adically too close to a fixed subvariety without lying on it. The current work is motivated by the analogy between torsion points on semi-abelian varieties and special or CM points on Shimura varieties. We prove the analog of Tate and Voloch’s result in a power of the modular curve Y (1) on replacing torsion points by points corresponding to a product of elliptic curves with complex multiplication and ordinary reduction. Moreover, we show that the assumption on ordinary reduction is necessary.
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:Oxford University Press
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:25 Apr 2018 09:37
Deposited On:25 Apr 2018 09:37

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