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Field name	Details
Dewey Class	512.7
Title	Elliptic Curves and Arithmetic Invariants ([EBook]) / by Haruzo Hida.
Author	Hida, Haruzo
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer
Publication	, 2013.
Physical Details	XVIII, 449 pages : online resource.
Series	Springer monographs in mathematics 1439-7382
ISBN	9781461466574
Summary Note	This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including Î¼-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.Â 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 note	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 Lâvalues.- 9 p-Adic Hecke L-functions and their Î¼-invariants.-10. Toric Subschemes in a Split Formal Torus -- 11. Hecke Stable Subvariety is a Shimura Subvariety -- References -- Symbol Index -- Statement Index -- Subject Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-4614-6657-4
Links to Related Works	Subject References: Algebraic Geometry . Elliptic equations . Geometry, Algebraic . Number Theory . Authors: Hida, Haruzo . Corporate Authors: SpringerLink (Online service) . Series: Springer monographs in mathematics . Classification: 512.7 . 512.7 (DDC 23) .

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Elliptic Curves and Arithmetic Invariants

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