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Complex Multiplication

  • Joseph H. Silverman
  • John Tate
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

In this chapter we want to describe how points of finite order on certain elliptic curves can be used to generate interesting extension fields of ℚ. Here we mean points of finite order with arbitrary complex coordinates, not just the ones with rational coordinates that we studied in Chapter II. So we will need to use some basic theorems about extension fields and Galois theory, but nothing very fancy. We will start by reminding you of most of the facts we will be using, and you can look at any basic algebra text (such as Herstein [1] or Jacobson [1]) for the proofs and additional background material.

Keywords

Elliptic Curve Complex Multiplication Elliptic Curf Galois Group Finite Order 
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 1992

Authors and Affiliations

  • Joseph H. Silverman
    • 1
  • John Tate
    • 2
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of MathematicsUniversity of Texas at AustinAustinUSA

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