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Local Fields And Their Extensions: A Constructive Approach (translations Of Mathematical Monographs, Vol 121) by I.B. Fesenko, S.V. Vostokov; [translated from the Russian by Ivan B. Fesenko; translation edited by Simeon Ivanov] is a book available to read on EtoBox.

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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]. 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 Exte

Author

I.B. Fesenko, S.V. Vostokov; [translated from the Russian by Ivan B. Fesenko; translation edited by Simeon Ivanov]

Publisher

American Mathematical Society; Amer Mathematical Society

Published

1993

Language

EN

ISBN

9780821846131

Subjects

Mathematics, Stem