Elliptic curves and arithmetic invariants Haruzo Hida

Format:

Book

Author/Creator:

Hida, Haruzo

Series:

Springer monographs in mathematics

Springer monographs in mathematics 1439-7382

Language:

English

Subjects (All):

Curves, Elliptic.

Invariants.

Number theory.

Elliptic functions.

Mathematics.

Number Theory.

Algebraic Geometry.

Local Subjects:

Mathematics.

Number Theory.

Algebraic Geometry.

Physical Description:

1 online resource

Place of Publication:

New York, NY Springer ©2013

System Details:

PDF

text file

Summary:

This book can be regarded as an introductory text to the author's previous book p-Adic Automorphic Forms on Shimura Varieties. This text includes many examples and applications of the theory of modular curves and the corresponding Shimura varieties

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

Contents:

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 [mu]-invariants

10. Toric subschemes in a split formal torus

11. Hecke stable subvariety is a Shimura subvariety

Nontriviality of Arithmetic Invariants Elliptic Curves and Modular Forms Invariants, Shimura Variety, and Hecke Algebra Review of Scheme Theory Geometry of Variety Elliptic and Modular Curves over Rings Modular Curves as Shimura Variety Nonvanishing Modulo p of Hecke L-Values

p-Adic Hecke L-Functions and Their μ-Invariants Toric Subschemes in a Split Formal Torus Hecke Stable Subvariety Is a Shimura Subvariety.006m o d.

Notes:

Includes bibliographical references and indexes

Print version record

Other Format:

Print version Hida, Haruzo. Elliptic curves and arithmetic invariants

ISBN:

9781461466574

1461466571

1461466563

9781461466567

OCLC:

849513502

Access Restriction:

Restricted for use by site license