Elliptic Curves and Big Galois Representations

Daniel Delbourgo (Monash University, Victoria)

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English

Cambridge University Press
31 July 2008

Mathematics & Sciences; Number theory

Series: London Mathematical Society Lecture Note Series

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.

By: Daniel Delbourgo (Monash University Victoria)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: No. 356
Dimensions: Height: 227mm, Width: 153mm, Spine: 15mm
Weight: 410g
ISBN: 9780521728669
ISBN 10: 0521728665
Series: London Mathematical Society Lecture Note Series
Pages: 288
Publication Date: 31 July 2008
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Daniel Delbourgo is Senior Lecturer in the School of Mathematical Sciences at Monash University in Australia.

Reviews for Elliptic Curves and Big Galois Representations

This research monograph contains much that has not been published elsewhere, and will be useful for specialists in the field who want to catch up on the author's work. Neil P. Dummigan, Mathematical Reviews