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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

CM points on products of Drinfeld modular curves


Author: Florian Breuer
Journal: Trans. Amer. Math. Soc. 359 (2007), 1351-1374
MSC (2000): Primary 11G09; Secondary 14G35
Published electronically: September 19, 2006
MathSciNet review: 2262854
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Abstract: Let $ X$ be a product of Drinfeld modular curves over a general base ring $ A$ of odd characteristic. We classify those subvarieties of $ X$ which contain a Zariski-dense subset of CM points. This is an analogue of the André-Oort conjecture. As an application, we construct non-trivial families of higher Heegner points on modular elliptic curves over global function fields.


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Additional Information

Florian Breuer
Affiliation: Department of Mathematical Sciences, University of Stellenbosch, Stellenbosch, 7600, South Africa
Email: fbreuer@sun.ac.za

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04109-2
PII: S 0002-9947(06)04109-2
Keywords: Drinfeld modular curves, CM points, Andr\'e-Oort conjecture, Heegner points
Received by editor(s): September 20, 2004
Received by editor(s) in revised form: March 1, 2005
Published electronically: September 19, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.