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)


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.




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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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