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Noncommutative Iwasawa Main Conjectures Over Totally Real Fields: Munster, April 2011 by John Coates, Peter Schneider, Sujatha Ramdorai - Paperback
572.25 AED

Noncommutative Iwasawa Main Conjectures Over Totally Real Fields: Munster, April 2011 by John Coates, Peter Schneider, Sujatha Ramdorai - Paperback

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Category Type
Mathematics
ISBN
9783642443350
Author
John Coates, Peter Schneider, Sujatha Ramdorai
Publisher
Springer
Description:

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 ...

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    Specifications

    Category Type
    Mathematics
    ISBN
    9783642443350
    Languages
    English
    Item EAN
    2724437254413
    People
    Author
    John Coates, Peter Schneider, Sujatha Ramdorai
    Category Type
    Mathematics
    ISBN
    9783642443350
    Languages
    English
    Item EAN
    2724437254413
    People
    Author
    John Coates, Peter Schneider, Sujatha Ramdorai
    People
    Publisher
    Springer
    Technical Information
    Binding
    Paperback
    Languages and countries
    Book Language
    English
    Read more
  •  

    Description:

    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

    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 Features:
    • Category: Mathematics
    • Binding: Paperback
    • Language of Text: English
    • Author(s): John Coates, Peter Schneider, Sujatha Ramdorai
    • Publisher: Springer
    • ISBN: 9783642443350
    • Number of Pages: 208
    • Dimensions: 9.21 x 6.14 x 0.46 inches
 

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