UID:
almahu_9947366652502882
Umfang:
1 online resource (233 p.)
ISBN:
1-281-76646-1
,
9786611766467
,
0-08-087370-7
Serie:
Pure and applied mathematics; a series of monographs and textbooks ; v. 55
Inhalt:
Algebraic number fields
Anmerkung:
Description based upon print version of record.
,
Front Cover; Algebraic Number Fields; Copyright Page; Contents; Preface; Chapter I. Subrings of Fields; 1. Localization; 2. Integral Dependence; 3. Discrete Valuation Rings and Dedekind Rings; 4. Fractional Ideals and the Class Group; 5. Norms and Traces; 6. Extensions of Dedekind Rings; 7. Discriminant; 8. Norms of Ideals; 9. Cyclotomic Fields; 10. Lattices in Real Vector Spaces; 11. The Unit Theorem and Finiteness of the Class Number; Chapter II. Complete Fields; 1. Valuations; 2. Completions; 3. Extensions of Nonarchimedean Valuations; 4. Archimedean Valuations
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5. Local Norms and Traces and the Product FormulaChapter III. Decomposition Groups and the Artin Map; 1. Decomposition and Inertia Groups; 2. The Frobenius Automorphism; 3. The Artin Map for Abelian Extensions; Chapter IV. Analytic Methods; 1. Moduli and Ray Classes; 2. Dirichlet Series; 3. Characters of Abelian Groups; 4. L-Series and Product Representations; 5. Frobenius Density Theorem; Chapter V. Class Field Theory; 1. Cohomology of Cyclic Groups; 2. Preparations for the Second Inequality; 3. A Norm Index Computation; 4. The Fundamental Equality for Cyclic Extensions
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5. The Reciprocity Theorem6. Ideal Groups, Conductors, and Class Fields; 7. Reduction Steps Toward the Existence Theorem; 8. Kummer Extensions and The S-Unit Theorem; 9. The Existence Theorem; 10. Some Consequences of the Classification Theorem; 11. Preliminaries for the Norm Residue Map and the Conductor Theorem; 12. Norm Residue Symbol; 13. The Hilbert Class Field; Chapter VI. Application of the General Theory to Quadratic Fields; 1. The Conductor of Q(vd); 2. Two Examples; 3. The Extended Class Group; Appendix A. Normal Basis Theorem and Hilbert's Theorem 90
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Appendix B. Modules over Principal Ideal DomainsBibliography; Index
,
English
Weitere Ausg.:
ISBN 0-12-380250-4
Sprache:
Englisch
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