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

Serdica Mathematical Journal (2004)

- Volume: 30, Issue: 2-3, page 363-394
- ISSN: 1310-6600

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topChipchakov, I.. "Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory." Serdica Mathematical Journal 30.2-3 (2004): 363-394. <http://eudml.org/doc/219665>.

@article{Chipchakov2004,

abstract = {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.},

author = {Chipchakov, I.},

journal = {Serdica Mathematical Journal},

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; Brauer groups; character groups; local reciprocity laws},

language = {eng},

number = {2-3},

pages = {363-394},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory},

url = {http://eudml.org/doc/219665},

volume = {30},

year = {2004},

}

TY - JOUR

AU - Chipchakov, I.

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

JO - Serdica Mathematical Journal

PY - 2004

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 30

IS - 2-3

SP - 363

EP - 394

AB - 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.

LA - eng

KW - 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; Brauer groups; character groups; local reciprocity laws

UR - http://eudml.org/doc/219665

ER -

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