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Title: Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory
Authors: Chipchakov, I.
Keywords: Field Admitting (one-dimensional) Local Class Field Theory
Strictly Primarily Quasilocal Field
Henselian Valued Field
Brauer Group
Character Group
Norm Group
Galois Extension
Regular Group Formation
Issue Date: 2004
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 30, No 2-3, (2004), 363p-394p
Abstract: 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 of the local reciprocity law for such fields. It shows that, in contrast to the special cases of local fields or strictly PQL-fields algebraic over a given global field, the norm groups of finite separable extensions of the considered fields are not necessarily equal to norm groups of finite Galois extensions with Galois groups of easily accessible structure.
Description: 2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.
ISSN: 1310-6600
Appears in Collections:Volume 30 Number 2-3

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