Elliptic Curves over Local Fields

  • Joseph H. Silverman
Part of the Graduate Texts in Mathematics book series (GTM, volume 106)


In this chapter we study the group of rational points on an elliptic curve defined over a field which is complete with respect to a discrete valuation. We start with some basic facts concerning Weierstrass equations and “reduction modulo π”.This enables us to break our problem up into several pieces; and then by examining each piece individually, we will be able to deduce a great deal about the group of rational points as a whole. Unless explicitly stated otherwise, we will use the following notation.


Elliptic Curve Elliptic Curf Good Reduction Residue Field Finite Extension 
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Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • Joseph H. Silverman
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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