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Primes of superspecial reduction for QM abelian surfaces
Author(s) -
Baba Srinath,
Granath Håkan
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn008
Subject(s) - mathematics , abelian group , reduction (mathematics) , good reduction , pure mathematics , geometry , medicine , surgery
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.