Nonabelian Fundamental Groups and Iwasawa Theory
£62.00
Part of London Mathematical Society Lecture Note Series
 Editors:
 John Coates, University of Cambridge
 Minhyong Kim, University College London
 Florian Pop, University of Pennsylvania
 Mohamed Saïdi, University of Exeter
 Peter Schneider, Universität Münster
 Date Published: December 2011
 availability: In stock
 format: Paperback
 isbn: 9781107648852
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Number theory currently has at least three different perspectives on nonabelian phenomena: the Langlands programme, noncommutative Iwasawa theory and anabelian geometry. In the second half of 2009, experts from each of these three areas gathered at the Isaac Newton Institute in Cambridge to explain the latest advances in their research and to investigate possible avenues of future investigation and collaboration. For those in attendance, the overwhelming impression was that number theory is going through a tumultuous period of theorybuilding and experimentation analogous to the late 19th century, when many different special reciprocity laws of abelian class field theory were formulated before knowledge of the Artin–Takagi theory. Nonabelian Fundamental Groups and Iwasawa Theory presents the state of the art in theorems, conjectures and speculations that point the way towards a new synthesis, an asyetundiscovered unified theory of nonabelian arithmetic geometry.
Read more Surveys the main ideas with the minimum of technical detail
 Explores relationships between various areas, which will inspire future research
 Encompasses a large portion of mainstream number theory
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×Product details
 Date Published: December 2011
 format: Paperback
 isbn: 9781107648852
 length: 320 pages
 dimensions: 228 x 152 x 15 mm
 weight: 0.45kg
 contains: 5 b/w illus.
 availability: In stock
Table of Contents
List of contributors
Preface
1. Lectures on anabelian phenomena in geometry and arithmetic Florian Pop
2. On Galois rigidity of fundamental groups of algebraic curves Hiroaki Nakamura
3. Around the Grothendieck anabelian section conjecture Mohamed Saïdi
4. From the classical to the noncommutative Iwasawa theory (for totally real number fields) Mahesh Kakde
5. On the ΜH(G)conjecture J. Coates and R. Sujatha
6. Galois theory and Diophantine geometry Minhyong Kim
7. Potential modularity  a survey Kevin Buzzard
8. Remarks on some locally Qpanalytic representations of GL2(F) in the crystalline case Christophe Breuil
9. Completed cohomology  a survey Frank Calegari and Matthew Emerton
10. Tensor and homotopy criteria for functional equations of ladic and classical iterated integrals Hiroaki Nakamura and Zdzisław Wojtkowiak.
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