Descent and Galois Cohomology

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

Abstract

Central to the proof of the Mordell theorem is the idea of descent which was present in the criterion for a group to be finitely generated, see 6(1.4). This criterion was based on the existence of a norm which came out of the theory of heights and the finiteness of the index (E(Q) :2E(Q)), or more generally (E(k) : nE(k)). In this chapter we will study the finiteness of these indices from the point of view of Galois cohomology with the hope of obtaining a better hold on the rank of E(Q), see 6(3.3). These indices are orders of the cokernel of multiplication by n and along the same line we consider the cokernel of the isogeny \( E[a,b]\xrightarrow{\varphi }E[ - 2a,\;{a^2} - 4b]\).

Keywords

Exact Sequence Elliptic Curve Homogeneous Space Rational Point Elliptic Curf 
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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