Geodesic
A group-theoretical property of the ramification filtration
Izvestiya. Mathematics, Tome 62 (1998) no. 6, pp. 1073-1094 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $\Gamma(p)$ be the Galois group of the maximal $p$-extension of a complete discrete valuation field with a perfect residue field of characteristic $p>0$. If $v_0>-1$ and $\Gamma(p)^{(v_0)}$ is the ramification subgroup of $\Gamma(p)$ in the upper numbering, we prove that any closed non-open finitely generated subgroup of the quotient $\Gamma(p)/\Gamma(p)^{(v_0)}$ is a free pro-$p$-group. In particular, this quotient has no torsion and no non-trivial commuting elements. 
@article{IM2_1998_62_6_a0,
     author = {V. A. Abrashkin},
     title = {A~group-theoretical property of the ramification filtration},
     journal = {Izvestiya. Mathematics},
     pages = {1073--1094},
     year = {1998},
     volume = {62},
     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1998_62_6_a0/}
}
TY  - JOUR
AU  - V. A. Abrashkin
TI  - A group-theoretical property of the ramification filtration
JO  - Izvestiya. Mathematics
PY  - 1998
SP  - 1073
EP  - 1094
VL  - 62
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/IM2_1998_62_6_a0/
LA  - en
ID  - IM2_1998_62_6_a0
ER  - 
%0 Journal Article
%A V. A. Abrashkin
%T A group-theoretical property of the ramification filtration
%J Izvestiya. Mathematics
%D 1998
%P 1073-1094
%V 62
%N 6
%U http://geodesic.mathdoc.fr/item/IM2_1998_62_6_a0/
%G en
%F IM2_1998_62_6_a0
V. A. Abrashkin. A group-theoretical property of the ramification filtration. Izvestiya. Mathematics, Tome 62 (1998) no. 6, pp. 1073-1094. http://geodesic.mathdoc.fr/item/IM2_1998_62_6_a0/

[1] Abrashkin V. A., “Filtratsiya vetvleniya gruppy Galua lokalnogo polya”, Tr. S.-P. Matem. ob-va, 3 (1995), 47–127 | MR | Zbl

[2] Abrashkin V. A., “Filtratsiya vetvleniya gruppy Galua lokalnogo polya, II”, Tr. MI RAN, 208 (1995), 18–69 | MR | Zbl

[3] Abrashkin V. A., Ramification filtration of the Galois group of a local field, III, Preprint / MPI 96-103 | MR

[4] Deligne P., “Les corps locaux de caracterisque $p$, limites de corps locaux de caracterisque 0”, Representations des groups reductifs sur un corps local, Travaux en Cours, Hermann, Paris, 1984, 120–157 | MR

[5] Gordeev N. L., “Beskonechnost chisla sootnoshenii v gruppe Galua maksimalnogo $p$-rasshireniya lokalnogo polya s ogranichennym vetvleniem”, Izv. AN SSSR. Ser. matem., 45 (1981), 592–607 | MR | Zbl

[6] Mauss E., “Relationen in Verzweigungsgruppen”, J. reine ang. Math., 258 (1973), 23–50 | MR

[7] Serre J.-P., Corps locaux, Hermann, Paris, 1968 | MR

[8] Wintenberger J.-P., “Le corps des normes de certaines extensions infinies des corps locaux; application”, Ann. Sci. Ec. Norm. Super. Ser. IV, 16 (1983), 59–89 | MR | Zbl

[9] Gordeev N., “Gruppy vetvleniya beskonechnykh $p$-rasshirenii lokalnogo polya”, Zapiski nauch. sem. LOMI, 71, Nauka, L., 1977, 96–132 | MR | Zbl