Elliptic Curves and Arithmetic Invariants (Springer Monographs in Mathematics)

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en Limba Engleză Carte Paperback – 08 Feb 2015
This introduction to Shimura varieties covers key topics including non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; elliptic and modular curves over rings and more.
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ISBN-13: 9781489990921
ISBN-10: 1489990925
Pagini: 468
Dimensiuni: 155 x 235 x 25 mm
Greutate: 0.65 kg
Ediția: 2013
Editura: Springer
Colecția Springer
Seria Springer Monographs in Mathematics

Locul publicării: New York, NY, United States

Public țintă



“The main aim of the book is to give an account of Hida’s results on arithmetic invariants in an accessible way. … The book is intended for mathematicians with some background on modular forms and is worthwhile for both graduate students and experts. … There are numerous examples, exercises, and remarks, all aimed at carefully helping the reader. In conclusion, this book is a very welcome addition to the mathematical literature.” (Florian Sprung, Mathematical Reviews, April, 2015)
“The author gives in this book a detailed account of results concerning arithmetic invariants, including µ-invariant and L-invariant. … it contains a detailed account of the author’s recent results concerning arithmetic invariants. The book, addressed to advanced graduate students and experts working in number theory and arithmetic geometry, is a welcome addition to this beautiful and difficult area of research.” (Andrzej Dąbrowski, zbMATH, Vol. 1284, 2014)


​​​​​​​​​​​​Contains top-notch research that will interest both experts and advanced graduate students
Written by an expert renowned for his discovery that modular forms fall into families, otherwise known as "Hida families"
Limits material to elliptic modular curves and the corresponding Shimura curves in order to make the book more accessible to graduate students​
Includes many exercises, examples, and applications that provide motivation for the reader