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Mathematics - Number Theory and Discrete Mathematics | Elliptic Curves and Arithmetic Invariants

Elliptic Curves and Arithmetic Invariants

Hida, Haruzo

2013, XVIII, 449 p.

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  • ​​​​​​​​​​​​Contains top-notch research that will interest both experts and advanced graduate students
  • Written by an expert renowned for his discovery that modular forms fall into families, otherwise known as "Hida families"
  • Limits material to elliptic modular curves and the corresponding Shimura curves in order to make the book more accessible to graduate students​
  • Includes many exercises, examples, and applications that provide motivation for the reader
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.

Content Level » Research

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

Related subjects » Algebra - Number Theory and Discrete Mathematics

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