Title Non-abelian Fundamental Groups and Iwasawa Theory

Published Cambridge : Cambridge University Press, 2011

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Description 1 online resource (322 pages) Series London Mathematical Society Lecture Note Series London Mathematical Society lecture note series. Contents 880-01 Cover; LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES; Title; Copyright; Contents; Contributors; Preface; Lectures on anabelian phenomena in geometry and arithmetic; Part I. Introduction and motivation; A. First examples; B. Galois characterization of global fields; Part II. Grothendieck's anabelian geometry; A. Warm-up: birational anabelian conjectures; B. Anabelian conjectures for curves; C. The section conjectures; Part III. Beyond the arithmetical action; A. Small Galois groups and valuations; B. Variation of fundamental groups in families of curves 880-01/(S 5 Analogue of the MH(G) conjecture for Hida families -- 6 Vanishing of the R-torsion -- References -- Galois theory and Diophantine geometry -- 1 The deficiency of abelian motives -- 2 Motivic fundamental groups and Selmer varieties -- 3 Diophantine finiteness -- 4 An explicit formula and speculations -- References -- Potential modularity -- a survey -- 1 Introduction -- 2 Semistable elliptic curves over Q are modular -- 3 Why the semistability assumption-- 4 All elliptic curves over Q are modular -- 5 Kisin's modularity lifting theorems -- 6 Generalisations to totally real fields -- 7 Potential modularity pre-Kisin and the p-λ trick -- 8 Potential modularity after Kisin -- 9 Some final remarks -- References -- Remarks on some locally Qp-analyticrep resentations of GL2(F) in the crystalline case -- 1 Introduction and notations -- 2 Quick review of the GL2(Qp)-case -- 3 Quick review of weakly admissible filtered φ-modules -- 4 Some locally Qp-analytic representations of GL2(F) -- 5 Weak admissibility and GL2(F)-unitarity I -- 6 Amice-Vélu and Vishik revisited -- 7 Weak admissibility and GL2(F)-unitarity II -- 8 Local-global considerations -- 9 The case where the Galois representation is reducible -- References -- Completed cohomology -- a survey -- 1 Definitions -- 2 Non-commutative Iwasawa theory -- 3 Poincaré duality -- 4 A simple example of everything so far -- 5 Congruence quotients of symmetric spaces -- 6 Conjectures on codimensions -- 7 Mod p analogues -- 8 Heuristics related to the p-adic Langlands programme -- References -- Tensor and homotopy criteria for functional equations of ℓ-adic and classical iterated integrals -- 1 Introduction -- 2 Multi-Kummer characters -- 3 Multi-Kummer duals -- 4 Iterated integrals and their functional equations -- 5 Case of polylogarithms -- 6 Examples -- References Summary Displays the intricate interplay between different foundations of non-commutative number theory Bibliography Includes bibliographical references Notes Print version record Subject Iwasawa theory. Non-Abelian groups. MATHEMATICS -- Number Theory. Iwasawa theory Non-Abelian groups Aufsatzsammlung Iwasawa-Theorie Nichtabelsche Gruppe Form Electronic book Author Kim, Minhyong Pop, Florian Saïdi, Mohamed Schneider, Peter ISBN 9781139221580 1139221582 9786613580474 6613580473 9781139225014 1139225014 1139218492 9781139218498 9780511984440 0511984448

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