Elliptic Curves and Arithmetic Invariants

• Main Author: Hida, Haruzo (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2013.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Algebraic geometry.; Number theory.; Number Theory.; Algebraic Geometry.

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...

Table of Contents:

• 1 Non-triviality 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 Non-vanishing Modulo p of Hecke L–values.- 9 p-Adic Hecke L-functions and their μ-invariants.- 10 Toric Subschemes in a Split Formal Torus
• 11 Hecke Stable Subvariety is a Shimura Subvariety
• References
• Symbol Index
• Statement Index
• Subject Index.