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Bulletin of the London Mathematical Society Advance Access originally published online on April 1, 2008
Bulletin of the London Mathematical Society 2008 40(2):311-318; doi:10.1112/blms/bdn008
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© 2008 London Mathematical Society

Primes of superspecial reduction for QM abelian surfaces

Srinath Baba

Department of Mathematics and Statistics
Concordia University
1455 de Maisonneuve Blvd West
Montréal
Quebec
Canada H3G 1M8
sbaba@mathstat.concordia.ca

Håkan Granath

Department of Mathematics
Karlstad University
65188 Karlstad
Sweden

Received 25 April 2006. Revision received 13 July 2007.

We show that any abelian surface with multiplication by the quaternion Q-algebra of discriminant 6, with field of moduli Q and which is a Jacobian in characteristic 2 and 3, has infinitely many primes of superspecial reduction. This is done by examining complex multiplication points in characteristic 0 and p and the values of a certain j-function on the associated moduli space at these points.

The first author was partially supported by NSERC. The second author was supported by a Marie Curie Intra-European Fellowship under the Sixth Framework Programme of the European Commission (MEIF-CT-2004-501793).

2000 Mathematics Subject Classification 11G18, 14G35, 11G25.


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