Nonabelian 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  Status/Location:

Loading...
Options
Location  Notes  Your Loan Policy 

Details
 Subjects:
 Iwasawa theory.
NonAbelian groups.  Form/Genre:
 Electronic books.
 Language:
 English
 Summary:
 Displays the intricate interplay between different foundations of noncommutative 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. Warmup: 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. Prol abelianbycentral birational anabelian geometryD. The Ihara/OdaMatsumoto 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 padic 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 padic Lie extensions5 Analogue of the MH(G) conjecture for Hida families; 6 Vanishing of the Rtorsion; 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 preKisin and the p? trick; 8 Potential modularity after Kisin; 9 Some final remarks; References; Remarks on some locally Qpanalyticrep 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 fmodules; 4 Some locally Qpanalytic representations of GL2(F); 5 Weak admissibility and GL2(F)unitarity I; 6 AmiceVélu and Vishik revisited; 7 Weak admissibility and GL2(F)unitarity II; 8 Localglobal 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:
 1107232376
0511984448
1280485493
1139223291
9786613580474
1139218492
113921540X
1139225014
1139221582  OCLC:
 775870071