Galois Cohomology and Isomorphism Classification of Elliptic Curves over Arbitrary Fields

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

Abstract

In Chapter 3 we saw that j(E) is an isomorphism invariant for elliptic Curves defined over algebraically closed fields. In this chapter we describe all elliptic curves over a given field k which become isomorphic over k sthe separable algebraic closure of k up to k isomorphism. This is done using the Galois group of k s over k and its action on the automorphism group of the elliptic curve over k s. The answer is given in terms of a certain first Galois cohomology set which is closely related to quadratic extensions of the field k.

Keywords

Exact Sequence Elliptic Curve Elliptic Curf Galois Group Short Exact Sequence 
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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