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

Chipchakov, 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 -