Elliptic Curves and Big Galois Representations Contributor(s): Delbourgo, Daniel (Author) |
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ISBN: 0521728665 ISBN-13: 9780521728669 Publisher: Cambridge University Press OUR PRICE: $84.54 Product Type: Paperback - Other Formats Published: September 2008 Annotation: Describes the arithmetic of modular forms and elliptic curves; self-contained and ideal for both graduate students and professional number theorists. |
Additional Information |
BISAC Categories: - Mathematics | Number Theory |
Dewey: 516.352 |
LCCN: 2008021192 |
Series: London Mathematical Society Lecture Notes |
Physical Information: 0.7" H x 6" W x 8.8" (0.92 lbs) 288 pages |
Descriptions, Reviews, Etc. |
Publisher Description: The arithmetic properties of modular forms and elliptic curves lie at the heart of modern number theory. This book develops a generalisation of the method of Euler systems to a two-variable deformation ring. The resulting theory is then used to study the arithmetic of elliptic curves, in particular the Birch and Swinnerton-Dyer (BSD) formula. Three main steps are outlined: the first is to parametrise 'big' cohomology groups using (deformations of) modular symbols. Finiteness results for big Selmer groups are then established. Finally, at weight two, the arithmetic invariants of these Selmer groups allow the control of data from the BSD conjecture. As the first book on the subject, the material is introduced from scratch; both graduate students and professional number theorists will find this an ideal introduction. Material at the very forefront of current research is included, and numerical examples encourage the reader to interpret abstract theorems in concrete cases. |