Tame and purely wild extensions of valued fields

Ershov, Yu.

doi:10.1090/S1061-0022-08-01019-4

Tame and purely wild extensions of valued fields
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by 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.

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