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The Resource Noncommutative Iwasawa Main Conjectures over Totally Real Fields : Münster, April 2011, edited by John Coates, Peter Schneider, R. Sujatha, Otmar Venjakob, (electronic resource)
Noncommutative Iwasawa Main Conjectures over Totally Real Fields : Münster, April 2011, edited by John Coates, Peter Schneider, R. Sujatha, Otmar Venjakob, (electronic resource)
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The item Noncommutative Iwasawa Main Conjectures over Totally Real Fields : Münster, April 2011, edited by John Coates, Peter Schneider, R. Sujatha, Otmar Venjakob, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Noncommutative Iwasawa Main Conjectures over Totally Real Fields : Münster, April 2011, edited by John Coates, Peter Schneider, R. Sujatha, Otmar Venjakob, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 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 noncommutative Iwasawa theory for many motives. Noncommutative Iwasawa theory has emerged dramatically over the last decade, culminating in the recent proof of the noncommutative main conjecture for the Tate motive over a totally real padic 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 noncommutative main conjecture were discovered by Venjakob, and were then systematically developed in the subsequent papers by CoatesFukayaKatoSujathaVenjakob and FukayaKato. 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 nonabelian 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 nonabelian 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 selfcontained 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
 Language
 eng
 Extent
 XI, 206 p. 71 illus., 1 illus. in color.
 Contents

 Preface
 John Coates, Dohyeong Kim: Introduction to the work of M. Kakde on the noncommutative main conjectures for totally real fields
 R. Sujatha: Reductions of the main conjecture
 Ted Chinburg, Georgios Pappas, Martin J. Taylor: The group logarithm past and present
 Peter Schneider, Otmar Venjakob: K_1 of certain Iwasawa algebras, after Kakde
 Mahesh Kakde: Congruences between abelian padic zeta functions
 Otmar Venjakob: On the work of Ritter and Weiss in comparison with Kakde's approach
 Malte Witte: Noncommutative Main Conjectures of Geometric Iwasawa Theory
 Isbn
 9783642321993
 Label
 Noncommutative Iwasawa Main Conjectures over Totally Real Fields : Münster, April 2011
 Title
 Noncommutative Iwasawa Main Conjectures over Totally Real Fields
 Title remainder
 Münster, April 2011
 Statement of responsibility
 edited by John Coates, Peter Schneider, R. Sujatha, Otmar Venjakob
 Language
 eng
 Summary
 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 noncommutative Iwasawa theory for many motives. Noncommutative Iwasawa theory has emerged dramatically over the last decade, culminating in the recent proof of the noncommutative main conjecture for the Tate motive over a totally real padic 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 noncommutative main conjecture were discovered by Venjakob, and were then systematically developed in the subsequent papers by CoatesFukayaKatoSujathaVenjakob and FukayaKato. 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 nonabelian 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 nonabelian 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 selfcontained 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
 http://library.link/vocab/creatorName
 Coates, John
 Image bit depth
 0
 LC call number
 QA241247.5
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName

 Schneider, Peter.
 Sujatha, R.
 Venjakob, Otmar.
 SpringerLink
 Series statement
 Springer Proceedings in Mathematics & Statistics,
 Series volume
 29
 http://library.link/vocab/subjectName

 Mathematics
 Geometry, algebraic
 Ktheory
 Number theory
 Mathematics
 Number Theory
 Algebraic Geometry
 KTheory
 Label
 Noncommutative Iwasawa Main Conjectures over Totally Real Fields : Münster, April 2011, edited by John Coates, Peter Schneider, R. Sujatha, Otmar Venjakob, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Preface  John Coates, Dohyeong Kim: Introduction to the work of M. Kakde on the noncommutative main conjectures for totally real fields  R. Sujatha: Reductions of the main conjecture  Ted Chinburg, Georgios Pappas, Martin J. Taylor: The group logarithm past and present  Peter Schneider, Otmar Venjakob: K_1 of certain Iwasawa algebras, after Kakde  Mahesh Kakde: Congruences between abelian padic zeta functions  Otmar Venjakob: On the work of Ritter and Weiss in comparison with Kakde's approach  Malte Witte: Noncommutative Main Conjectures of Geometric Iwasawa Theory
 Dimensions
 unknown
 Extent
 XI, 206 p. 71 illus., 1 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783642321993
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783642321993
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783642321993
 Label
 Noncommutative Iwasawa Main Conjectures over Totally Real Fields : Münster, April 2011, edited by John Coates, Peter Schneider, R. Sujatha, Otmar Venjakob, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Preface  John Coates, Dohyeong Kim: Introduction to the work of M. Kakde on the noncommutative main conjectures for totally real fields  R. Sujatha: Reductions of the main conjecture  Ted Chinburg, Georgios Pappas, Martin J. Taylor: The group logarithm past and present  Peter Schneider, Otmar Venjakob: K_1 of certain Iwasawa algebras, after Kakde  Mahesh Kakde: Congruences between abelian padic zeta functions  Otmar Venjakob: On the work of Ritter and Weiss in comparison with Kakde's approach  Malte Witte: Noncommutative Main Conjectures of Geometric Iwasawa Theory
 Dimensions
 unknown
 Extent
 XI, 206 p. 71 illus., 1 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783642321993
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783642321993
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783642321993
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