Real Points on Shimura Curves

  • Andrew P. Ogg
Part of the Progress in Mathematics book series (PM, volume 35)


Let B be a quaternion algebra over Q, i.e., a central simple alegbra of dimension 4 over Q. We assume that, B is indefinite, and fix an identification of B = BR with M 2(R). The discriminant D of B is then the product of an even number of distinct primes. The completion B p = BQ p , is a skew field if p | D and is isomorphic to M 2(Q p ) if p × D, and D = 1 if and only if B is isomorphic to M 2(Q), i.e., B is not a skew field.


Hyperelliptic Curve Real Point Quaternion Algebra Single Orbit Hyperelliptic Involution 
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Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • Andrew P. Ogg
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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