Geodesic
On the algebraic closure of a~local field for~$p=2$
Izvestiya. Mathematics , Tome 6 (1972) no. 5, pp. 925-937.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $k$ be a finite extension of the field of 2-adic numbers. In this paper we determine the structure of the Galois groups of the algebraic closure and of the maximal extension without simple ramification of the field $k$ under the assumption that the maximal extension without higher ramification of the field $k$ contains a fourth root of 1. 
@article{IM2_1972_6_5_a1,
     author = {I. G. Zel'venskii},
     title = {On the algebraic closure of a~local field for~$p=2$},
     journal = {Izvestiya. Mathematics },
     pages = {925--937},
     publisher = {mathdoc},
     volume = {6},
     number = {5},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_5_a1/}
}
TY  - JOUR
AU  - I. G. Zel'venskii
TI  - On the algebraic closure of a~local field for~$p=2$
JO  - Izvestiya. Mathematics 
PY  - 1972
SP  - 925
EP  - 937
VL  - 6
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1972_6_5_a1/
LA  - en
ID  - IM2_1972_6_5_a1
ER  - 
%0 Journal Article
%A I. G. Zel'venskii
%T On the algebraic closure of a~local field for~$p=2$
%J Izvestiya. Mathematics 
%D 1972
%P 925-937
%V 6
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1972_6_5_a1/
%G en
%F IM2_1972_6_5_a1
I. G. Zel'venskii. On the algebraic closure of a~local field for~$p=2$. Izvestiya. Mathematics , Tome 6 (1972) no. 5, pp. 925-937. http://geodesic.mathdoc.fr/item/IM2_1972_6_5_a1/

[1] Yakovlev A. V., “Gruppa Galua algebraicheskogo zamykaniya lokalnogo polya”, Izv. AN SSSR. Ser. matem., 32:6 (1968), 1283–1322 | Zbl

[2] Shafarevich I. R., “Obschii zakon vzaimnosti”, Matem. sb., 26 (68):1 (1950), 113–146 | Zbl

[3] Kneser M., “Zum expliziten Reziprozitätsgesetz von I. R. Šafarevič”, Math. Nachr., 6:2 (1951), 89–96 | DOI | MR | Zbl

[4] Demushkin S. P., “O 2-rasshireniyakh lokalnogo polya”, Sib. matem. zh., 4:4 (1963), 951–955

[5] Koch H., Galoissche Theorie der $p$-Erweiterungen, Berlin, 1970 | MR

[6] Koch H., “Über Galoissche Gruppen von $p$-adischen Zahlkörpern”, Math. Nachr., 29:1/2 (1965), 77–111 | DOI | MR | Zbl