Displaying similar documents to “Completely normal elements in some finite abelian extensions”

A survey of computational class field theory

Henri Cohen (1999)

Journal de théorie des nombres de Bordeaux

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We give a survey of computational class field theory. We first explain how to compute ray class groups and discriminants of the corresponding ray class fields. We then explain the three main methods in use for computing an equation for the class fields themselves: Kummer theory, Stark units and complex multiplication. Using these techniques we can construct many new number fields, including fields of very small root discriminant.

Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

Chipchakov, I. (2004)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20. This paper gives a characterization of Henselian discrete valued fields whose finite abelian extensions are uniquely determined by their norm groups and related essentially in the same way as in the classical local class field theory. It determines the structure of the Brauer groups and character groups of Henselian discrete valued strictly primary quasilocal (or PQL-) fields, and thereby, describes the forms...