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Automorphisms and reduction of Heegner points on Shimura curves at Cerednik-Drinfeld primes


Authors: Santiago Molina and Victor Rotger
Journal: Proc. Amer. Math. Soc. 142 (2014), 381-390
MSC (2010): Primary 11G18; Secondary 14G35
DOI: https://doi.org/10.1090/S0002-9939-2013-11772-7
Published electronically: October 24, 2013
MathSciNet review: 3133980
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Abstract: Let $ X$ be a Shimura curve of genus at least 2. Exploiting Čerednik-Drinfeld's description of the special fiber of $ X$ and the specialization of its Heegner points, we show that under certain technical conditions, the group of automorphisms of $ X$ corresponds to its group of Atkin-Lehner involutions.


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Additional Information

Santiago Molina
Affiliation: Department of Mathematics, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
Address at time of publication: Université du Luxembourg, Faculté des Sciences, de la Technologie et de la Communication, 6, rue Richard Coudenhove-Kalergi, L-1359 Luxembourg
Email: santiago.molina@uni.lu

Victor Rotger
Affiliation: Department of Applied Mathematics II, Universitat Politècnica de Catalunya, Barcelona, Spain
Email: victor.rotger@upc.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-11772-7
Received by editor(s): October 24, 2011
Received by editor(s) in revised form: January 23, 2012, and March 20, 2012
Published electronically: October 24, 2013
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.