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• catalog contributor b4503596.
• catalog contributor b4503597.
• catalog created "c1993.".
• catalog date "1993".
• catalog date "c1993.".
• catalog dateCopyrighted "c1993.".
• catalog description "4. The Milnor ring of a local field -- Appendix A. Absolute Galois group of a local field -- Appendix B. Multidimensional local fields.".
• catalog description "4. The reciprocity map [Psi][subscript F]. 5. Pairings of the multiplicative group. 6. The Existence Theorem. 7. Hazewinkel's theory and Dwork's theorem -- Ch. V. Local Class Field Theory. II. 1. The multipllcative group and abelian extensions. 2. Additive polynomials. 3. Normic subgroups -- Ch. VI. The Group of Units in a p-adic Field. 1. Formal power series. 2. The Artin-Hass-Shafarevich map. 3. Series related to primitive roots. 4. Primary elements. 5. The Shafarevich decomposition -- Ch. VII. Explicit Formulas for the Hilbert Norm Residue Symbol. 1. Origin of formulas. 2. The pairing [actual symbol not reproducible]. 3. Kummer's extensions of a p-adic field. 4. Explicit formulas. 5. Applications and generalizations -- Ch. VIII. Explicit Formulas for the Hilbert Pairing on Formal Groups. 1. Formal groups. 2. Generalized Hilbert pairing -- Ch. IX. The Milnor K-groups of a Local Field. 1. The Milnor ring of a field. 2. The Milnor ring of a discrete valuation field. 3. The norm map.".
• catalog description "Ch. I. Complete Discrete Valuation Fields. 1. Ultrametric absolute values. 2. Valuations and valuation fields. 3. Discrete valuation fields. 4. Completion. 5. Filtrations of discrete valuation fields. 6. The group of principal units as a Z[subscript p]-module. 7. Set of multiplicative representatives. 8. The Witt ring. 9. Artin-Hasse maps -- Ch. II. Extensions of Discrete Valuation Fields. 1. The Hensel Lemma and Henselian fields. 2. Extensions of valuation fields. 3. Unramified and ramified extensions. 4. Galois extensions. 5. Structure theorems for complete fields -- Ch. III. The Norm Map. 1. Cyclic extensions of prime degree. 2. Artin-Schreier extensions. 3. The Hasse-Herbrand function. 4. The norm and ramification groups. 5. The field of norms -- Ch. IV. Local Class Field Theory. I. 1. Complete discrete valuation fields with finite residue field. 2. The Neukirch map [Upsilon][subscript L/F]. 3. Functorial properties of [Upsilon][subscript L/F].".
• catalog description "Includes bibliographical references and index.".
• catalog extent "xv, 283 p. ;".
• catalog hasFormat "Local fields and their extensions.".
• catalog identifier "0821846132 (acid-free)".
• catalog isFormatOf "Local fields and their extensions.".
• catalog isPartOf "Translations of mathematical monographs, 0065-9282 ; v. 121".
• catalog issued "1993".
• catalog issued "c1993.".
• catalog language "eng rus".
• catalog language "eng".
• catalog publisher "Providence, R.I. : American Mathematical Society,".
• catalog relation "Local fields and their extensions.".
• catalog subject "512/.74 20".
• catalog subject "Algebraic fields.".
• catalog subject "Field extensions (Mathematics)".
• catalog subject "QA247 .F47 1993".
• catalog tableOfContents "4. The Milnor ring of a local field -- Appendix A. Absolute Galois group of a local field -- Appendix B. Multidimensional local fields.".
• catalog tableOfContents "4. The reciprocity map [Psi][subscript F]. 5. Pairings of the multiplicative group. 6. The Existence Theorem. 7. Hazewinkel's theory and Dwork's theorem -- Ch. V. Local Class Field Theory. II. 1. The multipllcative group and abelian extensions. 2. Additive polynomials. 3. Normic subgroups -- Ch. VI. The Group of Units in a p-adic Field. 1. Formal power series. 2. The Artin-Hass-Shafarevich map. 3. Series related to primitive roots. 4. Primary elements. 5. The Shafarevich decomposition -- Ch. VII. Explicit Formulas for the Hilbert Norm Residue Symbol. 1. Origin of formulas. 2. The pairing [actual symbol not reproducible]. 3. Kummer's extensions of a p-adic field. 4. Explicit formulas. 5. Applications and generalizations -- Ch. VIII. Explicit Formulas for the Hilbert Pairing on Formal Groups. 1. Formal groups. 2. Generalized Hilbert pairing -- Ch. IX. The Milnor K-groups of a Local Field. 1. The Milnor ring of a field. 2. The Milnor ring of a discrete valuation field. 3. The norm map.".
• catalog tableOfContents "Ch. I. Complete Discrete Valuation Fields. 1. Ultrametric absolute values. 2. Valuations and valuation fields. 3. Discrete valuation fields. 4. Completion. 5. Filtrations of discrete valuation fields. 6. The group of principal units as a Z[subscript p]-module. 7. Set of multiplicative representatives. 8. The Witt ring. 9. Artin-Hasse maps -- Ch. II. Extensions of Discrete Valuation Fields. 1. The Hensel Lemma and Henselian fields. 2. Extensions of valuation fields. 3. Unramified and ramified extensions. 4. Galois extensions. 5. Structure theorems for complete fields -- Ch. III. The Norm Map. 1. Cyclic extensions of prime degree. 2. Artin-Schreier extensions. 3. The Hasse-Herbrand function. 4. The norm and ramification groups. 5. The field of norms -- Ch. IV. Local Class Field Theory. I. 1. Complete discrete valuation fields with finite residue field. 2. The Neukirch map [Upsilon][subscript L/F]. 3. Functorial properties of [Upsilon][subscript L/F].".
• catalog title "Local fields and their extensions : a constructive approach / I.B. Fesenko, S.V. Vostokov ; [translated from the Russian by Ivan B. Fesenko ; translation edited by Simeon Ivanov].".
• catalog type "text".