ebook9781461466574d4325

Description

This book contains a detailed account of the result of the author’s recent Annals paper and JAMS paper on arithmetic invariant, including Œº-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.