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

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 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.

Partially supported by Grant MM1106/2001 of the Bulgarian Foundation for Scientific Research.