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Local class field theory
Author(s):
Yu.
L.
Ershov
Translated by:
B. M. Bekker
Original publication:
Algebra i Analiz,
tom 15
(2003),
vypusk 6.
Journal:
St. Petersburg Math. J.
15
(2004),
837-846.
MSC (2000):
Primary 11R37
Posted:
November 16, 2004
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Abstract:
New sufficient conditions for the validity of local class field theory for Henselian valued fields are established. An example is presented to show that these conditions are less restrictive than the applicability of the Neukirch abstract class field theory.
References:
-
- 1.
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- 2.
- J. Neukirch, Algebraic number theory, Grundehren Math. Wiss., vol. 322, Springer-Verlag, Berlin, 1999, Chapter IV. MR 1697859 (2000m:11104)
- 3.
- Yu. L. Ershov, Abstract class field theory (a finitary approach), Mat. Sb. 194 (2003), no. 2, 37-60; English transl., Sb. Math. 194 (2003), no. 1-2, 199-223. MR 1992148 (2004f:11131)
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- O. F. G. Schilling, The theory of valuations, Math. Surveys, vol. 4, Amer. Math. Soc., Providence, RI, 1950. MR 0043776 (13:315b)
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- P. Draxl, Ostrowski's theorem for Henselian valued skew fields, J. Reine Angew. Math. 354 (1984), 213-218. MR 0767581 (86g:12008)
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- R. Pierce, Associative algebras, Grad. Texts in Math., vol. 88, Springer-Verlag, New York-Berlin, 1982. MR 0674652 (84c:16001)
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Additional Information:
Yu.
L.
Ershov
Affiliation:
Sobolev Mathematical Institute, Akademik Koptyug Ave., Novosibirsk 630090, Russia
Email:
ershov@math.nsc.ru
DOI:
10.1090/S1061-0022-04-00834-9
PII:
S 1061-0022(04)00834-9
Keywords:
Class field theory,
Henselian valued field,
$z$-group
Received by editor(s):
10/OCT/2002
Posted:
November 16, 2004
Copyright of article:
Copyright
2004,
American Mathematical Society
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