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