Elliptic Curves and Big Galois Representations
By (author) Daniel Delbourgo
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Elliptic Curves and Big Galois Representations by Daniel Delbourgo
Book DescriptionThe 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.
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Book DetailsISBN: 9780521728669
(228mm x 152mm x 15mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 31-Jul-2008
Country of Publication: United Kingdom
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Author Biography - Daniel Delbourgo
Daniel Delbourgo is Senior Lecturer in the School of Mathematical Sciences at Monash University in Australia.
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