Habegger, Philipp. (2014) The TateVoloch conjecture in a power of a modular curve. International Mathematics Research Notices, 2014 (12). pp. 33033339.
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Abstract
Let p be a prime. Tate and Voloch proved that a point of finite order in the algebraic torus cannot be padically too close to a fixed subvariety without lying on it. The current work is motivated by the analogy between torsion points on semiabelian 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 
ISSN:  10737928 
eISSN:  16870247 
Note:  Publication type according to Uni Basel Research Database: Journal article 
Identification Number: 

Last Modified:  25 Apr 2018 09:37 
Deposited On:  25 Apr 2018 09:37 
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