Overview

Number theory currently has at least three different perspectives on non-abelian phenomena: the Langlands programme, non-commutative 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 theory-building 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. Non-abelian 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 as-yet-undiscovered unified theory of non-abelian arithmetic geometry.

Full Product Details

Author:   John Coates (University of Cambridge) ,  Minhyong Kim (University College London) ,  Florian Pop (University of Pennsylvania) ,  Mohamed Saïdi (University of Exeter)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press (Virtual Publishing)
Volume:   393
ISBN:  

9780511984440

ISBN 10:   0511984448
Publication Date:   05 January 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Undefined
Publisher's Status:   Active
Availability:   Available To Order  
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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 Qp-analytic 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 l-adic and classical iterated integrals Hiroaki Nakamura and Zdzisław Wojtkowiak.

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Author Information

John Coates is Sadleirian Professor of Pure Mathematics at the University of Cambridge. Minhyong Kim is Professor of Pure Mathematics in the Department of Mathematics at University College London. Florian Pop is a Professor of Mathematics at the University of Pennsylvania. Mohamed Saidi is an Associate Professor in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter. Peter Schneider is a Professor in the Mathematical Institute at the University of Münster.

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