Elliptic Curves and Arithmetic Invariants, 1st Edition

  • Published By:
  • ISBN-10: 1461466571
  • ISBN-13: 9781461466574
  • DDC: 516.3
  • Grade Level Range: College Freshman - College Senior
  • 449 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

  • Price:  Sign in for price



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.

Table of Contents

Front Cover.
Other Frontmatter.
Title Page.
Copyright Page.
1: Nontriviality of Arithmetic Invariants.
2: Elliptic Curves and Modular Forms.
3: Invariants, Shimura Variety, and Hecke Algebra.
4: Review of Scheme Theory.
5: Geometry of Variety.
6: Elliptic and Modular Curves over Rings.
7: Modular Curves as Shimura Variety.
8: Nonvanishing Modulo p of Hecke L-Values.
9: p-Adic Hecke L-Functions and Their ¼-Invariants.
10: Toric Subschemes in a Split Formal Torus.
11: Hecke Stable Subvariety is a Shimura Subvariety.
Symbol Index.
Statement Index.
Subject Index.