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Tame and purely wild extensions of valued fields
Author(s):
Yu.
L.
Ershov
Translated by:
B. M. Bekker
Original publication:
Algebra i Analiz,
tom 19
(2007),
nomer 5.
Journal:
St. Petersburg Math. J.
19
(2008),
765-773.
MSC (2000):
Primary 12F15
Posted:
June 25, 2008
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Abstract:
A systematic and concise exposition of the basic results concerning two complementary classes (tame and purely wild) of extensions of (Henselian) valued fields is given. These notions proved to be quite useful both for the general theory and for the model theory of such fields. Along with new results, new proofs of old results are presented. Thus, in the proof of the well-known Pank theorem on the existence of a complement to the ramification group in the absolute Galois group of a Henselian valued field, the properties of maximal immediate extensions are employed instead of cohomological methods.
References:
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- 1.
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- 2.
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- 3.
- F.-V. Kuhlmann, M. Pank, and P. Roquette, Immediate and purely wild extensions of valued fields, Manuscripta Math. 55 (1986), no. 1, 39-67. MR 0828410 (87d:12012)
- 4.
- F.-V. Kuhlmann, Henselian function fields and tame fields, Heidelberg, 1994 (manuscript).
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Additional Information:
Yu.
L.
Ershov
Affiliation:
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, 4 Acad. Koptyug Avenue, 630090 Novosibirsk, Russia
Email:
ershov@math.nsc.ru
DOI:
10.1090/S1061-0022-08-01019-4
PII:
S 1061-0022(08)01019-4
Keywords:
Henselian valued fields,
valuation ring,
valuation group,
ramified extension,
totally unramified extension
Received by editor(s):
20/APR/2007
Posted:
June 25, 2008
Additional Notes:
Partially supported by the Council on Grants of President of the Russian Federation for the state support of leading scientific schools (project no. NSh-4787.2006.1)
Dedicated:
Dedicated to the centenary of the birth of the outstanding Russian mathematician D.K.Faddeev
Copyright of article:
Copyright
2008,
American Mathematical Society
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