Titlebook: Local Fields; Jean-Pierre Serre Textbook 1979 Springer Science+Business Media New York 1979 Fields.Lokaler Körper.algebra.algebraic geomet

overbearing

Galois CohomologyLet K/. be a finite Galois extension with Galois group G. The group G acts both on the additive group of K and on the multiplicative group K*; hence we can investigate the corresponding cohomology groups.

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Brauer Group of a Local FieldThroughout this chapter, K denotes a field complete under a valuation υ, A denotes the valuation ring of υ, and . the residue field.

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Local Class Field TheoryStandard local class field theory is concerned with complete fields K whose residue field . is finite.

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https://doi.org/10.1007/978-1-4757-5673-9Fields; Lokaler Körper; algebra; algebraic geometry; algebraic number field; arithmetic; cohomology; field;

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Graduate Texts in Mathematicshttp://image.papertrans.cn/l/image/587628.jpg

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Class Formationsthe cohomological aspect of class field theory, both in the local and the global cases. The present chapter is restricted to the main properties of class formations; the reader will find in Artin-Tate [8] further developments (the Šafarevič theorem, Weil groups).

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