Tame and purely wild extensions of valued fields
Algebra i analiz, Tome 19 (2007) no. 5, pp. 124-136.

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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.
Keywords: Henselian valued fields, valuation ring, valuation group, ramified extension, totally unramified extension.
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Yu. L. Ershov. Tame and purely wild extensions of valued fields. Algebra i analiz, Tome 19 (2007) no. 5, pp. 124-136. http://geodesic.mathdoc.fr/item/AA_2007_19_5_a4/

[1] Ershov Yu. L., Kratno normirovannye polya, Nauch. kn., Novosibirsk, 2000

[2] Leng S., Algebra, Mir, M., 1968

[3] Kuhlmann F.-V., Pank M., Roquette P., “Immediate and purely wild extensions of valued fields”, Manuscripta Math., 55:1 (1986), 39–67 | DOI | MR | Zbl

[4] Kuhlmann F.-V., Henselian function fields and tame fields, manuscript, Heidelberg, 1994

[5] Zarisskii O., Samyuel P., Kommutativnaya algebra, T. 2, IL, M., 1963

[6] Engler A. J., Prestel A., Valued fields, Springer-Verlag, Berlin, 2005 | MR

[7] Melnikov O. V., Tavgen O. I., “Absolyutnaya gruppa Galua genzeleva polya”, Dokl. AN BSSR, 29:7 (1985), 581–583 | MR