Elliptic Curves pp 152-161 | Cite as

# Descent and Galois Cohomology

## 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**) :2*E*(**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## Preview

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