Elliptic Curves and Arithmetic Invariants

  • Haruzo Hida

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Haruzo Hida
    Pages 43-82
  3. Haruzo Hida
    Pages 145-216
  4. Haruzo Hida
    Pages 217-224
  5. Haruzo Hida
    Pages 225-279
  6. Haruzo Hida
    Pages 281-334
  7. Haruzo Hida
    Pages 335-365
  8. Haruzo Hida
    Pages 387-403
  9. Back Matter
    Pages 427-449

About this book

Introduction

This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including μ-invariant, L-invariant, and similar topics.   This book can be regarded as an introductory text to the author's previous book p-Adic Automorphic Forms on Shimura Varieties.  Written as a down-to-earth introduction to Shimura varieties, this text includes many examples and applications of the theory that provide motivation for the reader.  Since it is limited to modular curves and the corresponding Shimura varieties, this book is not only a great resource for experts in the field, but it is also accessible to advanced graduate students studying number theory.  Key topics include non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; scheme theory; elliptic and modular curves over rings; and Shimura curves.

Keywords

Hecke algebra Shimura variety arithmetic invariants elliptic curves modular forms scheme theory

Authors and affiliations

  • Haruzo Hida
    • 1
  1. 1.Department of MathematicsUniversity of California, Los AngelesLos AngelesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-6657-4
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-6656-7
  • Online ISBN 978-1-4614-6657-4
  • Series Print ISSN 1439-7382
  • About this book
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