Non-abelian Fundamental Groups and Iwasawa Theory

Non-abelian Fundamental Groups and Iwasawa Theory

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Description

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.show more

Product details

  • Electronic book text | 320 pages
  • CAMBRIDGE UNIVERSITY PRESS
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • 5 b/w illus.
  • 1139211986
  • 9781139211987

About Professor John Coates

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 Munster.show more

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 Saidi; 4. From the classical to the noncommutative Iwasawa theory (for totally real number fields) Mahesh Kakde; 5. On the à H(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 Zdzislaw Wojtkowiak.show more