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OverviewThe 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. Full Product DetailsAuthor: J. Coates , R. SujathaPublisher: Narosa Publishing House Imprint: Narosa Publishing House Edition: 2nd Revised edition ISBN: 9788184870237ISBN 10: 818487023 Pages: 112 Publication Date: 02 March 2010 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsPreface / Notation / Basic Results from Galois Cohomology / The Iwasawa Theory of the Selmer Group / The Euler Characteristic Formula / Numerical Examples over the Cyclotomic Zp-extension of Q / Numerical Examples Over Q / Appendix / Bibliography.ReviewsAuthor InformationJ. Coates.: University of Cambridge, Cambridge, U.K. R. Sujatha.: Tata Institute of Fundamental Research, Mumbai Tab Content 6Author Website:Countries AvailableAll regions |