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Galois Cohomology of Elliptic Curves , Second Edition

	Galois Cohomology Of Elliptic Curves , Second Edition by J. Coates, R. Sujatha
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The genesis of these notes was a series of four lectures given by the first author at the Tata Institute of Fundamental Research. It evolved into a joint project and contains many improvements and extensions on the material covered in the original lectures. Let F be a finite extension of Q, and E an elliptic curve defined over F. The fundamental idea of the Iwasawa theory of elliptic curves, which grew out of Iwasawa`s basic work on the ideal class groups of cyclotomic fields, is to study deep arithmetic questions about E over F, via the study of coarser questions about the arithmetic of E over various infinite extensions of F. These notes will mainly discuss the simplest non-trivial example of the Iwasawa theory of E over the cyclotomic Zp-extension of F. However, we also make some comments about the Iwasawa theory of E over the field obtained by adjoining all p-power division points on E to F. We have also discussed in detail a number of numerical examples. The only changes made to the original notes have been to take modest account of the considerable progress which has been made in non-commutative Iwasawa theory in the intervening years. We have also included a short section on the deep theorems of Kato on the cyclotomic Iwasawa theory of elliptic curves.

ISBN-9788184870237

Pages : 112