Non-abelian Fundamental Groups and Iwasawa Theory

doi:10.1017/CBO9780511984440

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Edited by John Coates, University of Cambridge, Minhyong Kim, University College London, Florian Pop, University of Pennsylvania, Mohamed Saïdi, University of Exeter, Peter Schneider, Universität Münster

Publisher:: Cambridge University Press
Online publication date:: January 2012
Print publication year:: 2011
Online ISBN:: 9780511984440
DOI:: https://doi.org/10.1017/CBO9780511984440

Subjects:: Mathematics (general), Mathematics, Number Theory, Geometry and Topology
Series:: London Mathematical Society Lecture Note Series (393)

64.99 (GBP)

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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.

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Non-abelian Fundamental Groups and Iwasawa Theory

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Frontmatter
pp i-iv

Contents
pp v-v

List of contributors
pp vi-vi

Preface
pp vii-x

Lectures on anabelian phenomena in geometry and arithmetic
pp 1-55

On Galois rigidity of fundamental groups of algebraic curves
pp 56-71

Around the Grothendieck anabelian section conjecture
pp 72-106

From the classical to the noncommutative Iwasawa theory (for totally real number fields)
pp 107-131

On the MH(G)-conjecture
pp 132-161

Galois theory and Diophantine geometry
pp 162-187

Potential modularity – a survey
pp 188-211

Remarks on some locally ℚp-analytic representations of GL2(F) in the crystalline case
pp 212-238

Completed cohomology – a survey
pp 239-257

Tensor and homotopy criteria for functional equations of ℓ-adic and classical iterated integrals
pp 258-310

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Non-abelian Fundamental Groups and Iwasawa Theory

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