PREFACE
INDEX OF NOTATION
1 TOPOLOGICAL GROUPS
1.1 Basic Notions
1.2 Haar Measure
1.3 Profinite Groups
1.4 Pro-p-Groups
Exercises
2 SOME REPRESENTATION THEORY
2.1 Representations of Locally Compact Groups
2.2 Banach Algebras and the Gelfand Transform
2.3 The Spectral Theorems
2.4 Unitary Representations
Exercises
3 DUALITY FOR LOCALLY COMPACT ABELIAN GROUPS
3.1 The Pontryagin Dual
3.2 Functions of Positive Type
3.3 The Fourier Inversion Formula
3.4 Pontryagin Duality
Exercises
4 THE STRUCTURE OF ARITHMETIC FIELDS
4.1 The Module of an Antomorphism
4.2 The Classification of Locally Compact Fields
4.3 Extensions of Local Fields
4.4 Places and Completions of Global Fields
4.5 Ramification and Bases
Exercises
5 ADELES, IDELES, AND THE CLASS GROUPS
5.1 Restricted Direct Products,Characters,and Measures
5.2 Adeles,Ideles,and the Approximation Theorem
5.3 The Geometry of AKIK
5.4 The Class Groups
Exercises
6 A QUICK TOUR OF CLASS FIELD THEORY
6.1 Frobenius Elements
6.2 The Tchebotarev Density Theorem
6.3 The Transfer Map
6.4 Artin’’s Reciprocity Law
6.5 Abelian Extensions of Q and Qp
Exercises
7 TATE』S THESIS AND APPLICATIONS
APPENDICES
REFERENCES
INDEX
