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Elliptic Curves over Global Fields and -Adic Representations

  • Dale Husemöller
Part of the Graduate Texts in Mathematics book series (GTM, volume 111)

Abstract

In the previous two chapters the local study of elliptic curves was carried out and a substantial part of the theory was related to how the fundamental symmetry, the Frobenius element, behaved on the curve modulo a prime. For an elliptic curve E over a number field K (or more generally any global field), we have for each prime a Frobenius element acting on certain points of the curve. These Frobenius elements are in Gal(K s/K), and this Galois group acts on the K s-valued points E(K s) on the group N E = N E(K s), the subgroup of N-division points, and on the limit Tate modules T (E) where N and are prime to the characteristic of K. In Chapters 12 and 13 the action of Gal(K s/K) on the endomorphisms EndK s(E) and the automorphisms AutK s(E) over K s was considered in detail. As usual K s denotes a separable algebraic closure of K.

Keywords

Elliptic Curve Elliptic Curf Galois Group Abelian Variety Number Field 
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 1987

Authors and Affiliations

  • Dale Husemöller
    • 1
  1. 1.Department of MathematicsHaverford CollegeHaverfordUSA

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