By Jürgen Neukirch

the current manuscript is a better variation of a textual content that first seemed lower than a similar identify in Bonner Mathematische Schriften, no.26, and originated from a chain of lectures given through the writer in 1965/66 in Wolfgang Krull's seminar in Bonn. Its major objective is to supply the reader, accustomed to the fundamentals of algebraic quantity concept, a brief and fast entry to classification box concept. This script comprises 3 components, the 1st of which discusses the cohomology of finite teams. the second one half discusses neighborhood classification box thought, and the 3rd half issues the category box conception of finite algebraic quantity fields.

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