UID:
almahu_9949697925202882
Format:
1 online resource (555 p.)
ISBN:
1-283-52550-X
,
9786613837950
,
0-08-095416-2
Series Statement:
North-Holland mathematical library ; v. 8
Uniform Title:
Sūron.
Content:
This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field.
Note:
Translation of Suron.
,
Front Cover; The Theory of Numbers, Volume 8; Copyright Page; Contents; Preface; Table of notations; CHAPTER I. Cohomology of Groups; 1. Tensor products and groups of homomorphisms; 2. Homology and cohomology; 3. Inhomogeneous complexes b(g); 4. Subgroups and related cohomology groups; 5. Tensor products and cup products; 6. Cohomology theory of finite groups; 7. Cohomology theory of cyclic groups; 8. Tate's Theorem and Galois cohomology; CHAPTER II. Valuation Theory; 1. Valuations of fields; 2. Complete fields; 3. Archimedean valuations; 4. Non-Archimedean valuations I
,
5. Non-Archimedean valuations II6. Hilbert's theory; 7. Discriminants and differents (local cases); 8. The differential of formal power series; CHAPTER III. Adele Rings and Idele Groups; 1. Locally compact groups; 2. Locally compact rings; 3. Local fields; 4. Adele and idele; 5. Extensions of the base field; 6. The structure of adele rings; 7. The structure of idele groups; CHAPTER IV. The Main Theorems of Class Field Theory; 1. Cyclotomic fields; 2. Kummer fields; 3. Power residue symbols and Hilbert norm residue symbols
,
4. Quadratic number fields and the reciprocity laws for quadratic residues5. Artin-Schreier fields; 6. The theory of infinite Galois extensions; 7. Main theorems of the class field theory; CHAPTER V. Proofs of the Main Theorems; 1. Local cases; 2. Proofs of the conductor theorems; 3. The first inequality; 4. The second inequality and the existence theorem; 5. The Reciprocity Law; 6. Weil groups; APPENDIX 1. Ideal Theory; 1. Ideals in a Dedekind domain; 2. Discriminants and differents (global cases); 3. Artin-Whaples' theory; APPENDIX 2. History of the Class Field Theory
,
1. From Euclid to Hilbert2. Takagi and Artin's class field theory; 3. The development of the theory after Takagi and Artin; Bibliography; Index
,
English
Additional Edition:
ISBN 0-444-10678-2
Language:
English
