Franklin

Non-abelian fundamental groups and Iwasawa theory [electronic resource] / edited by John Coates ... [et al.].

Publication:
Cambridge ; New York : Cambridge University Press, 2012.
Format/Description:
Book
1 online resource (322 p.)
Series:
London Mathematical Society lecture note series ; 393.
London Mathematical Society lecture note series ; 393
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Subjects:
Iwasawa theory.
Non-Abelian groups.
Form/Genre:
Electronic books.
Language:
English
Summary:
Displays the intricate interplay between different foundations of non-commutative number theory.
Contents:
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
C. Pro-l abelian-by-central birational anabelian geometryD. The Ihara/Oda-Matsumoto conjecture; Some major open questions/problems; Bibliography; On Galois rigidity of fundamental groups of algebraic curves; English translation of [31] (1989); Complementary notes; References; Around the Grothendieck anabelian section conjecture; Introduction; 1 Generalities on arithmetic fundamental groups and sections; 2 Grothendieck anabelian section conjecture; 3 Good sections of arithmetic fundamental groups; 4 Cuspidalisation of sections of arithmetic fundamental groups
5 Applications to the Grothendieck anabelian section conjecture6 On a weak form of the p-adic Grothendieck anabelian section conjecture; References; From the classical to the noncommutative Iwasawa theory (for totally real number fields); 1 Introduction; 2 The set up; 3 The classical main conjecture; 4 Definition of K0 and K1; 5 The theory of determinants; 6 Generalised Iwasawa main conjecture; 6.1 Known results; 7 Generalisations; References; On the MH(G)-conjecture; 1 Introduction; 2 Statement of the conjecture; 3 Additional evidence for the MH(G)-conjecture
4 Hida families over p-adic Lie extensions5 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 fields7 Potential modularity pre-Kisin and the p-? 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 f-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
Notes:
Description based upon print version of record.
Includes bibliographical references.
Contributor:
Coates, J.
ISBN:
1-107-23237-6
0-511-98444-8
1-280-48549-3
1-139-22329-1
9786613580474
1-139-21849-2
1-139-21540-X
1-139-22501-4
1-139-22158-2
OCLC:
775870071