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catalog contributor b12571915.
catalog contributor b12571916.
catalog created "c2002.".
catalog date "2002".
catalog date "c2002.".
catalog dateCopyrighted "c2002.".
catalog description "235 -- 1. Origin of Formulas 235 -- 2. The Pairing <., .> 241 -- 3. Explicit Class Field Theory for Kummer Extensions 250 -- 4. Explicit Formulas 255 -- 5. Applications and Generalizations 258 -- Chapter VIII. Explicit Formulas for Hilbert Pairings on Formal Groups 267 -- 1. Formal Groups 267 -- 2. Generalized Hilbert Pairing for Lubin-Tate Groups 272 -- 3. Generalized Hilbert Pairing for Honda Groups 276 -- Chapter IX. The Milnor K-groups of a Local Field 283 -- 1. The Milnor Ring of a Field 283 -- 2. The Milnor Ring of a Discrete Valuation Field 286 -- 3. The Norm Map 293 -- 4. The Milnor Ring of a Local Field 304.".
catalog description "95 -- Chapter IV. Local Class Field Theory. I 111 -- 1. Useful Results on Local Fields 112 -- 2. The Neukirch Map 123 -- 3. The Hazewinkel Homomorphism 128 -- 4. The Reciprocity Map 139 -- 5. Pairings of the Multiplicative Group 142 -- 6. The Existence Theorem 153 -- 7. Other Approaches to the Local Reciprocity Map 161 -- 8. Nonabelian Extensions 165 -- Chapter V. Local Class Field Theory. II 171 -- 1. The Multiplicative Group and Abelian Extensions 171 -- 2. Additive Polynomials 179 -- 3. Normic Subgroups 187 -- 4. Local p-Class Field Theory 196 -- 5. Generalizations 203 -- Chapter VI. The Group of Units of Local Number Fields 207 -- 1. Formal Power Series 207 -- 2. The Artin-Hasse-Shafarevich Map 214 -- 3. Series Associated to Roots 219 -- 4. Primary Elements 228 -- 5. The Shafarevich Basis 232 -- Chapter VII. Explicit Formulas for the Hilbert Symbol".
catalog description "Chapter I. Complete Discrete Valuation Fields 1 -- 1. Ultrametric Absolute Values 1 -- 2. Valuations and Valuation Fields 4 -- 3. Discrete Valuation Fields 6 -- 4. Completion 9 -- 5. Filtrations of Discrete Valuation Fields 12 -- 6. The Group of Principal Units as a Z[subscript p]-module 17 -- 7. Set of Multiplicative Representatives 22 -- 8. The Witt ring 26 -- 9. Artin-Hasse Maps 29 -- Chapter II. Extensions of Discrete Valuation Fields 35 -- 1. The Hensel Lemma and Henselian Fields 35 -- 2. Extensions of Valuation Fields 39 -- 3. Unramified and Ramified Extensions 49 -- 4. Galosis Extensions 56 -- 5. Structure Theorems for Complete Fields 61 -- Chapter III. The Norm Map 67 -- 1. Cyclic Extensions of Prime Degree 67 -- 2. Artin-Schreier Extensions 74 -- 3. The Hasse-Herbrand Function 79 -- 4. The Norm and Ramification Groups 88 -- 5. The Field of Norms".
catalog description "Includes bibliographical references (p. 319-339) and index.".
catalog extent "xi, 345 p. ;".
catalog identifier "082183259X (alk. paper)".
catalog isPartOf "Translations of mathematical monographs, 0065-9282 ; v. 121".
catalog issued "2002".
catalog issued "c2002.".
catalog language "eng".
catalog publisher "Providence, R.I. : American Mathematical Society,".
catalog subject "512/.74 21".
catalog subject "Algebraic fields.".
catalog subject "Field extensions (Mathematics)".
catalog subject "QA247 .F47 2002".
catalog tableOfContents "235 -- 1. Origin of Formulas 235 -- 2. The Pairing <., .> 241 -- 3. Explicit Class Field Theory for Kummer Extensions 250 -- 4. Explicit Formulas 255 -- 5. Applications and Generalizations 258 -- Chapter VIII. Explicit Formulas for Hilbert Pairings on Formal Groups 267 -- 1. Formal Groups 267 -- 2. Generalized Hilbert Pairing for Lubin-Tate Groups 272 -- 3. Generalized Hilbert Pairing for Honda Groups 276 -- Chapter IX. The Milnor K-groups of a Local Field 283 -- 1. The Milnor Ring of a Field 283 -- 2. The Milnor Ring of a Discrete Valuation Field 286 -- 3. The Norm Map 293 -- 4. The Milnor Ring of a Local Field 304.".
catalog tableOfContents "95 -- Chapter IV. Local Class Field Theory. I 111 -- 1. Useful Results on Local Fields 112 -- 2. The Neukirch Map 123 -- 3. The Hazewinkel Homomorphism 128 -- 4. The Reciprocity Map 139 -- 5. Pairings of the Multiplicative Group 142 -- 6. The Existence Theorem 153 -- 7. Other Approaches to the Local Reciprocity Map 161 -- 8. Nonabelian Extensions 165 -- Chapter V. Local Class Field Theory. II 171 -- 1. The Multiplicative Group and Abelian Extensions 171 -- 2. Additive Polynomials 179 -- 3. Normic Subgroups 187 -- 4. Local p-Class Field Theory 196 -- 5. Generalizations 203 -- Chapter VI. The Group of Units of Local Number Fields 207 -- 1. Formal Power Series 207 -- 2. The Artin-Hasse-Shafarevich Map 214 -- 3. Series Associated to Roots 219 -- 4. Primary Elements 228 -- 5. The Shafarevich Basis 232 -- Chapter VII. Explicit Formulas for the Hilbert Symbol".
catalog tableOfContents "Chapter I. Complete Discrete Valuation Fields 1 -- 1. Ultrametric Absolute Values 1 -- 2. Valuations and Valuation Fields 4 -- 3. Discrete Valuation Fields 6 -- 4. Completion 9 -- 5. Filtrations of Discrete Valuation Fields 12 -- 6. The Group of Principal Units as a Z[subscript p]-module 17 -- 7. Set of Multiplicative Representatives 22 -- 8. The Witt ring 26 -- 9. Artin-Hasse Maps 29 -- Chapter II. Extensions of Discrete Valuation Fields 35 -- 1. The Hensel Lemma and Henselian Fields 35 -- 2. Extensions of Valuation Fields 39 -- 3. Unramified and Ramified Extensions 49 -- 4. Galosis Extensions 56 -- 5. Structure Theorems for Complete Fields 61 -- Chapter III. The Norm Map 67 -- 1. Cyclic Extensions of Prime Degree 67 -- 2. Artin-Schreier Extensions 74 -- 3. The Hasse-Herbrand Function 79 -- 4. The Norm and Ramification Groups 88 -- 5. The Field of Norms".
catalog title "Local fields and their extensions / I.B. Fesenko, S.V. Vostokov.".
catalog type "text".