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.