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010   $a1-4614-6657-1
024 7 $a10.1007/978-1-4614-6657-4
035   $a(OCoLC)849513502
035   $a(MiFhGG)GVRL6YJG
035   $a(CKB)2560000000103548
035   $a(MiAaPQ)EBC1317402
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100   $a20130411d2013      uy         0
101 0 $aeng
135   $aurun|---uuuua
181   $ctxt
182   $cc
183   $acr
200 10$aElliptic curves and arithmetic invariants /$fHaruzo Hida
205   $a1st ed. 2013.
210   $aNew York $cSpringer$d2013
215   $a1 online resource (xviii, 449 pages) $cillustrations
225 0 $aSpringer Monographs in Mathematics
300   $a"ISSN: 1439-7382."
311   $a1-4899-9092-5 
311   $a1-4614-6656-3 
320   $aIncludes bibliographical references and index.
327   $a1 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 ?-invariants.- 10 Toric Subschemes in a Split Formal Torus -- 11 Hecke Stable Subvariety is a Shimura Subvariety  -- References -- Symbol Index -- Statement Index -- Subject Index.
330   $aThis book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including ?-invariant, L-invariant, and similar topics.   This book can be regarded as an introductory text to the author's previous book p-Adic Automorphic Forms on Shimura Varieties.  Written as a down-to-earth introduction to Shimura varieties, this text includes many examples and applications of the theory that provide motivation for the reader.  Since it is limited to modular curves and the corresponding Shimura varieties, this book is not only a great resource for experts in the field, but it is also accessible to advanced graduate students studying number theory.  Key topics include non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; scheme theory; elliptic and modular curves over rings; and Shimura curves.
410  0$aSpringer monographs in mathematics.
606   $aNumber theory
606   $aElliptic functions
615  0$aNumber theory.
615  0$aElliptic functions.
676   $a516.352
700   $aHida$b Haruzo$062786
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910438135703321
996   $aElliptic Curves and Arithmetic Invariants$92515931
997   $aUNINA