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Noncommutative Iwasawa Main Conjectures over Totally Real Fields - 9783642443350
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Item specifics
- Condition
- Book Title
- Noncommutative Iwasawa Main Conjectures over Totally Real Fields
- ISBN
- 9783642443350
- Publication Year
- 2014
- Type
- Textbook
- Format
- Paperback
- Language
- English
- Publication Name
- Noncommutative Iwasawa Main Conjectures over Totally Real Fields: Munster, April 2011
- Item Height
- 235mm
- Publisher
- Springer-Verlag Berlin AND Heidelberg Gmbh & Co. KG
- Item Width
- 155mm
- Subject
- Mathematics
- Item Weight
- 3401g
- Number of Pages
- 208 Pages
About this product
Product Information
The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives. Non-commutative Iwasawa theory has emerged dramatically over the last decade, culminating in the recent proof of the non-commutative main conjecture for the Tate motive over a totally real p-adic Lie extension of a number field, independently by Ritter and Weiss on the one hand, and Kakde on the other. The initial ideas for giving a precise formulation of the non-commutative main conjecture were discovered by Venjakob, and were then systematically developed in the subsequent papers by Coates-Fukaya-Kato-Sujatha-Venjakob and Fukaya-Kato. There was also parallel related work in this direction by Burns and Flach on the equivariant Tamagawa number conjecture. Subsequently, Kato discovered an important idea for studying the K_1 groups of non-abelian Iwasawa algebras in terms of the K_1 groups of the abelian quotients of these Iwasawa algebras. Kakde's proof is a beautiful development of these ideas of Kato, combined with an idea of Burns, and essentially reduces the study of the non-abelian main conjectures to abelian ones. The approach of Ritter and Weiss is more classical, and partly inspired by techniques of Frohlich and Taylor. Since many of the ideas in this book should eventually be applicable to other motives, one of its major aims is to provide a self-contained exposition of some of the main general themes underlying these developments. The present volume will be a valuable resource for researchers working in both Iwasawa theory and the theory of automorphic forms.
Product Identifiers
Publisher
Springer-Verlag Berlin AND Heidelberg Gmbh & Co. KG
ISBN-13
9783642443350
eBay Product ID (ePID)
209662740
Product Key Features
Publication Name
Noncommutative Iwasawa Main Conjectures over Totally Real Fields: Munster, April 2011
Format
Paperback
Language
English
Subject
Mathematics
Publication Year
2014
Type
Textbook
Number of Pages
208 Pages
Dimensions
Item Height
235mm
Item Width
155mm
Volume
29
Item Weight
3401g
Additional Product Features
Series Title
Springer Proceedings in Mathematics & Statistics
Editor
Otmar Venjakob, John Coates, R. Sujatha, Peter Schneider
Country/Region of Manufacture
Germany
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eBay item number:354836287176
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