Geodesic
Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory
Serdica Mathematical Journal, Tome 30 (2004) no. 2-3, pp. 363-394

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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.
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 
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     author = {Chipchakov, I.},
     title = {Henselian {Discrete} {Valued} {Fields} {Admitting} {One-Dimensional} {Local} {Class} {Field} {Theory}},
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Chipchakov, I. Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory. Serdica Mathematical Journal, Tome 30 (2004) no. 2-3, pp. 363-394. http://geodesic.mathdoc.fr/item/SMJ2_2004_30_2-3_a13/