Tame and purely wild extensions of valued fields
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Yu. L. Ershov
Translated by: B. M. Bekker - St. Petersburg Math. J. 19 (2008), 765-773
- DOI: https://doi.org/10.1090/S1061-0022-08-01019-4
- Published electronically: 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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Bibliographic 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
- Received by editor(s): April 20, 2007
- Published electronically: 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)
- © Copyright 2008 American Mathematical Society
- Journal: St. Petersburg Math. J. 19 (2008), 765-773
- MSC (2000): Primary 12F15
- DOI: https://doi.org/10.1090/S1061-0022-08-01019-4
- MathSciNet review: 2381943
Dedicated: Dedicated to the centenary of the birth of the outstanding Russian mathematician D. K. Faddeev