Non-abelian fundamental groups in Iwasawa theory
By: edited by John Coates ... [et al.].
Series: London Mathematical Society lecture note series -- 393
Publisher: Cambridge University Press
Published: 2011
Place of publication: Cambridge; New York
Language: eng
Number of pages: 310
ISBN-13: 9781107648852
Subjects: MATHEMATICS / Number Theory; Iwasawa theory; Non-Abelian groups
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"--
Table of contents: title: Machine generated contents note: 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 Sai;di; 4. From the classical to the noncommutative Iwasawa theory (for totally real number fields) Mahesh Kakde; 5. On the MH(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.