This text offers a modern exposition of the arithmetical properties of local fields using explicit and constructive tools and methods. It incorporates improvements to the first edition, with 60 additional pages reflecting several aspects of the developments in local number theory. The volume consists of four parts: elementary properties of local fields, class field theory for various types of local fields and generalizations, explicit formulas for the Hilbert pairing, and Milnor $K$-groups of fields and local fields. The ...
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This text offers a modern exposition of the arithmetical properties of local fields using explicit and constructive tools and methods. It incorporates improvements to the first edition, with 60 additional pages reflecting several aspects of the developments in local number theory. The volume consists of four parts: elementary properties of local fields, class field theory for various types of local fields and generalizations, explicit formulas for the Hilbert pairing, and Milnor $K$-groups of fields and local fields. The first three parts essentially simplify, revise, and update the first edition.
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