Elliptic Curves and Arithmetic Invariants

2013
ISBN: 978-1-4614-6656-7
Verlag: Springer US

Buch, Englisch, 450 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 8218 g

Reihe: Springer Monographs in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Hida, Haruzo

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

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.

Über Autor(innen)

Haruzo Hida is currently a professor of mathematics at University of California, Los Angeles.