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Galois Cohomology of Elliptic Curves: Second Edition
 
J. Coates Cambridge University, Cambridge, England
R. Sujatha Tate Institute of Fundamental Research, Mumbai, India
A publication of Tata Institute of Fundamental Research
Galois Cohomology of Elliptic Curves
Softcover ISBN:  978-81-8487-023-7
Product Code:  TIFR/2.R
List Price: $60.00
AMS Member Price: $48.00
Please note AMS points can not be used for this product
Galois Cohomology of Elliptic Curves
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Galois Cohomology of Elliptic Curves: Second Edition
J. Coates Cambridge University, Cambridge, England
R. Sujatha Tate Institute of Fundamental Research, Mumbai, India
A publication of Tata Institute of Fundamental Research
Softcover ISBN:  978-81-8487-023-7
Product Code:  TIFR/2.R
List Price: $60.00
AMS Member Price: $48.00
Please note AMS points can not be used for this product
  • Book Details
     
     
    Tata Institute of Fundamental Research Publications
    Volume: 22010; 103 pp
    MSC: Primary 11

    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 \(F\). At present, we only know how to formulate this Iwasawa theory when the infinite extension is a \(p\)-adic Lie extension for a fixed prime number \(p\). These notes will mainly discuss the simplest non-trivial example of the Iwasawa theory of \(E\) over the cyclotomic \(zp\)-extension of \(F\). However, the authors also make some comments about the Iwasawa theory of \(E\) over the field obtained by adjoining all \(p\)-power division points on \(E\) to \(F\). They discuss in detail a number of numerical examples, which illustrate the general theory beautifully. In addition, they outline some of the basic results in Galois cohomology which are used repeatedly in the study of the relevant Iwasawa modules.

    The only changes made to the original notes: The authors take modest account of the considerable progress which has been made in non-commutative Iwasawa theory in the intervening years. They also include a short section on the deep theorems of Kato on the cyclotomic Iwasawa theory of elliptic curves.

    A publication of the Tata Institute of Fundamental Research. Distributed worldwide except in India, Bangladesh, Bhutan, Maldavis, Nepal, Pakistan, and Sri Lanka.

    Readership

    Mathematicians interested in algebraic number theory.

  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 22010; 103 pp
MSC: Primary 11

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 \(F\). At present, we only know how to formulate this Iwasawa theory when the infinite extension is a \(p\)-adic Lie extension for a fixed prime number \(p\). These notes will mainly discuss the simplest non-trivial example of the Iwasawa theory of \(E\) over the cyclotomic \(zp\)-extension of \(F\). However, the authors also make some comments about the Iwasawa theory of \(E\) over the field obtained by adjoining all \(p\)-power division points on \(E\) to \(F\). They discuss in detail a number of numerical examples, which illustrate the general theory beautifully. In addition, they outline some of the basic results in Galois cohomology which are used repeatedly in the study of the relevant Iwasawa modules.

The only changes made to the original notes: The authors take modest account of the considerable progress which has been made in non-commutative Iwasawa theory in the intervening years. They also include a short section on the deep theorems of Kato on the cyclotomic Iwasawa theory of elliptic curves.

A publication of the Tata Institute of Fundamental Research. Distributed worldwide except in India, Bangladesh, Bhutan, Maldavis, Nepal, Pakistan, and Sri Lanka.

Readership

Mathematicians interested in algebraic number theory.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.