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Real Points on Shimura Curves

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

Abstract

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.

Keywords

Hyperelliptic Curve Real Point Quaternion Algebra Single Orbit Hyperelliptic Involution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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