Geodesic
The structure of the congruence kernel for $\mathrm{SL}_2$ in the case of a global field of positive characteristic
Sbornik. Mathematics, Tome 77 (1994) no. 2, pp. 489-495 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper the following description of the congruence kernel $C(\mathrm{SL}_2,\mathcal O)$ is given, where $\mathcal O$ is the coordinate ring of an affine curve obtained by removing a point from a projective curve over a finite field $k_0$. Theorem. {\it $C(\mathrm{SL}_2,\mathcal O)=(*_{x\in X}H_x)*P$ is the free profinite product over a separable space $X$ of groups $H_x$ that are isomorphic to the direct product $\prod\mathbb{Z}/p\mathbb{Z}$ of a continuum of groups of order $p=\operatorname{char}(k_0)$, and a separable projective group $P$ each of whose open subgroups is free. } The proof uses a general result on normal subgroups of free profinite products. 
@article{SM_1994_77_2_a13,
     author = {P. A. Zalesskii},
     title = {The structure of the~congruence kernel for~$\mathrm{SL}_2$ in the~case of a~global field of positive characteristic},
     journal = {Sbornik. Mathematics},
     pages = {489--495},
     year = {1994},
     volume = {77},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1994_77_2_a13/}
}
TY  - JOUR
AU  - P. A. Zalesskii
TI  - The structure of the congruence kernel for $\mathrm{SL}_2$ in the case of a global field of positive characteristic
JO  - Sbornik. Mathematics
PY  - 1994
SP  - 489
EP  - 495
VL  - 77
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1994_77_2_a13/
LA  - en
ID  - SM_1994_77_2_a13
ER  - 
%0 Journal Article
%A P. A. Zalesskii
%T The structure of the congruence kernel for $\mathrm{SL}_2$ in the case of a global field of positive characteristic
%J Sbornik. Mathematics
%D 1994
%P 489-495
%V 77
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1994_77_2_a13/
%G en
%F SM_1994_77_2_a13
P. A. Zalesskii. The structure of the congruence kernel for $\mathrm{SL}_2$ in the case of a global field of positive characteristic. Sbornik. Mathematics, Tome 77 (1994) no. 2, pp. 489-495. http://geodesic.mathdoc.fr/item/SM_1994_77_2_a13/

[1] Serre J.-P., “Le probleme des groupes de congruence pour $\operatorname {SL}_2 $”, Ann. Math., 92 (1970), 489–657 | DOI | MR

[2] Melnikov O. V., “Kongruents-yadro dlya $\operatorname {SL}_2$”, DAN SSSR, 17:3 (1976), 867–870 | Zbl

[3] Lubotzky A., “Free Quotients and the Congruence Kernel of $\operatorname {SL}_2 $”, J. Algebra, 77 (1982), 411–418 | DOI | MR | Zbl

[4] Zalesskii P. A., Melnikov O. V., “Podgruppy prokonechnykh grupp, deistvuyuschikh na derevyakh”, Matem. sb., 135(177) (1988), 419–439

[5] Zalesskii P. A., “Geometricheskaya kharakterizatsiya svobodnykh konstruktsii prokonechnykh grupp”, Sib. matem. zhurn., 30:2 (1989), 73–84 | MR | Zbl

[6] Zalesskii P. A., Melnikov O. V., “Fundamentalnye gruppy grafov prokonechnykh grupp”, Algebra i analiz, 1:4 (1989), 117–135 | MR

[7] Melnikov O. V., “Svobodnye prokonechnye proizvedeniya i gomologii”, Izv. AN SSSR. Ser. matem., 53:1 (1989), 97–120 | MR | Zbl

[8] Serre J.-P., Trees, Springer-Verlag, New York, 1980 | MR | Zbl

[9] Baumslag G., “On the residual finiteness of generalized free products of nilpotent groups”, Trans. Amer. Soc., 106 (1963), 193–209 | DOI | MR | Zbl

[10] Zalesskii P. A., “Prokonechnye gruppy bez svobodnykh neabelevykh podgrupp, deistvuyuschie na derevyakh”, Matem. sb., 181:1 (1990), 57–67

[11] Binz E., Neukirch J., Wenzel G., “A subgroup theorem for free products of profinite groups”, J. Algebra, 19:1 (1971), 104 | DOI | MR | Zbl

[12] Lubotzky A., Dries V. D., “Subgroup of free profinite groups and large subfields of $\widetilde {\mathbb Q}$”, Israel J. of Mathematics, 39:1–2, 25–42 | MR

[13] Melnikov O. V., “Proektivnye predely svobodnykh prokonechnykh grupp”, Dokl. AN BSSR, 24:11 (1980), 968–970 | MR | Zbl