Springer Proceedings in Mathematics & Statistics

Noncommutative Iwasawa Main Conjectures over Totally Real Fields

Münster, April 2011

Editors: Coates, J., Schneider, P., Ramdorai, S., Venjakob, O. (Eds.)

  • Includes  a self-contained and simplified proof of Kakde's main algebraic result, as well as introductory articles on related topics
  • Extremely useful for many years to come  
  • Will almost certainly lead to major research progress in both Iwasawa theory and the theory of automorphic forms​
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Hardcover 103,95 €
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Softcover 103,95 €
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  • ISBN 978-3-642-44335-0
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About this book

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.

Reviews

“Its aim was to present progress on noncommutative main conjectures for Iwasawa theory over totally real fields. … The number theory community has to thank the editors and the authors for their efforts which make these intriguing recent developments more widely accessible.” (C. Baxa, Monatshefte für Mathematik, Vo. 180, 2016)


Table of contents (7 chapters)

  • Introduction to the Work of M. Kakde on the Non-commutative Main Conjectures for Totally Real Fields

    Coates, John (et al.)

    Pages 1-22

    Preview Buy Chapter 30,19 €
  • Reductions of the Main Conjecture

    Sujatha, R.

    Pages 23-50

    Preview Buy Chapter 30,19 €
  • The Group Logarithm Past and Present

    Chinburg, Ted (et al.)

    Pages 51-78

    Preview Buy Chapter 30,19 €
  • K 1 of Certain Iwasawa Algebras, After Kakde

    Schneider, Peter (et al.)

    Pages 79-123

    Preview Buy Chapter 30,19 €
  • Congruences Between Abelian p-Adic Zeta Functions

    Kakde, Mahesh

    Pages 125-157

    Preview Buy Chapter 30,19 €

Buy this book

eBook 83,29 €
price for Spain (gross)
  • ISBN 978-3-642-32199-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 103,95 €
price for Spain (gross)
  • ISBN 978-3-642-32198-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 103,95 €
price for Spain (gross)
  • ISBN 978-3-642-44335-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Noncommutative Iwasawa Main Conjectures over Totally Real Fields
Book Subtitle
Münster, April 2011
Editors
  • John Coates
  • Peter Schneider
  • Sujatha Ramdorai
  • Otmar Venjakob
Series Title
Springer Proceedings in Mathematics & Statistics
Series Volume
29
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-32199-3
DOI
10.1007/978-3-642-32199-3
Hardcover ISBN
978-3-642-32198-6
Softcover ISBN
978-3-642-44335-0
Series ISSN
2194-1009
Edition Number
1
Number of Pages
XII, 208
Topics