Geodesic
Tame and purely wild extensions of valued fields
Algebra i analiz, Tome 19 (2007) no. 5, pp. 124-136 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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, ramified extension, totally unramified extension.
Mots-clés : valuation group 
@article{AA_2007_19_5_a4,
     author = {Yu. L. Ershov},
     title = {Tame and purely wild extensions of valued fields},
     journal = {Algebra i analiz},
     pages = {124--136},
     year = {2007},
     volume = {19},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2007_19_5_a4/}
}
TY  - JOUR
AU  - Yu. L. Ershov
TI  - Tame and purely wild extensions of valued fields
JO  - Algebra i analiz
PY  - 2007
SP  - 124
EP  - 136
VL  - 19
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/AA_2007_19_5_a4/
LA  - ru
ID  - AA_2007_19_5_a4
ER  - 
%0 Journal Article
%A Yu. L. Ershov
%T Tame and purely wild extensions of valued fields
%J Algebra i analiz
%D 2007
%P 124-136
%V 19
%N 5
%U http://geodesic.mathdoc.fr/item/AA_2007_19_5_a4/
%G ru
%F AA_2007_19_5_a4
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