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Elliptic Curves and Arithmetic Invariants

BuchGebunden
450 Seiten
Englisch
Springererschienen am09.06.2013
This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including μ-invariant, L-invariant, and similar topics.mehr
Verfügbare Formate
BuchGebunden
EUR149,79
BuchKartoniert, Paperback
EUR149,79
E-BookPDF1 - PDF WatermarkE-Book
EUR139,09

Produkt

KlappentextThis book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including μ-invariant, L-invariant, and similar topics.
ZusammenfassungThis 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.
Details
ISBN/GTIN978-1-4614-6656-7
ProduktartBuch
EinbandartGebunden
Verlag
Erscheinungsjahr2013
Erscheinungsdatum09.06.2013
ReiheSpringer Monographs in Mathematics
Seiten450 Seiten
SpracheEnglisch
Gewicht807 g
IllustrationenXVIII, 450 p.
Artikel-Nr.23439401

Inhalt/Kritik

Inhaltsverzeichnis
1 Non-triviality of Arithmetic Invariantsâ.- 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 μ-invariants.- 10 Toric Subschemes in a Split Formal Torus.- 11 Hecke Stable Subvariety is a Shimura Subvarietyâ.- References.- Symbol Index.- Statement Index.- Subject Index.mehr
Kritik
"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 Dabrowski, zbMATH, Vol. 1284, 2014)mehr