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Non-abelian Fundamental Groups and Iwasawa Theory

Non-abelian Fundamental Groups and Iwasawa Theory

£62.00

Part of London Mathematical Society Lecture Note Series

Florian Pop, Hiroaki Nakamura, Mohamed Saïdi, Mahesh Kakde, J. Coates, R. Sujatha, Minhyong Kim, Kevin Buzzard, Christophe Breuil, Frank Calegari, Matthew Emerton, Hiroaki Nakamura, Zdzisław Wojtkowiak
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  • 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 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.

    • 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 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.

  • Editors

    John Coates, University of Cambridge
    John Coates is Sadleirian Professor of Pure Mathematics at the University of Cambridge.

    Minhyong Kim, University College London
    Minhyong Kim is Professor of Pure Mathematics in the Department of Mathematics at University College London.

    Florian Pop, University of Pennsylvania
    Florian Pop is a Professor of Mathematics at the University of Pennsylvania.

    Mohamed Saïdi, University of Exeter
    Mohamed Saidi is an Associate Professor in the College of Engineering, Mathematics and Physical Sciences at the University of Exeter.

    Peter Schneider, Universität Münster
    Peter Schneider is a Professor in the Mathematical Institute at the University of Münster.

    Contributors

    Florian Pop, Hiroaki Nakamura, Mohamed Saïdi, Mahesh Kakde, J. Coates, R. Sujatha, Minhyong Kim, Kevin Buzzard, Christophe Breuil, Frank Calegari, Matthew Emerton, Hiroaki Nakamura, Zdzisław Wojtkowiak

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