Skip to content
Register Sign in Wishlist

Elliptic Curves and Big Galois Representations


Part of London Mathematical Society Lecture Note Series

  • Date Published: July 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521728669

£ 67.99

Add to cart Add to wishlist

Other available formats:

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
About the Authors
  • 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.

    • Self-contained; develops the material from basic level so accessible to first year graduate students
    • Exercises, diagrams and worked examples aid understanding and develop skills
    • Presents material at the very forefront of current research, equipping the reader to understand theorems at the cutting edge
    Read more

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: July 2008
    • format: Paperback
    • isbn: 9780521728669
    • length: 288 pages
    • dimensions: 227 x 153 x 15 mm
    • weight: 0.41kg
    • contains: 70 b/w illus. 1 table 5 exercises
    • availability: Available
  • Table of Contents

    List of notations
    1. Background
    2. p-adic L-functions and Zeta-elements
    3. Cyclotomic deformations of modular symbols
    4. A user's guide to Hida theory
    5. Crystalline weight deformations
    6. Super Zeta-elements
    7. Vertical and half-twisted arithmetic
    8. Diamond-Euler characteristics: the local case
    9. Diamond-Euler characteristics: the global case
    10. Two-variable Iwasawa theory of elliptic curves
    A. The primitivity of Zeta elements
    B. Specialising the universal path vector
    C. The weight-variable control theorem

  • Author

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

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.