Geodesic
Projectivity of the~Absolute Galois Groups of Multi-Valued Fields
Matematičeskie trudy, Tome 6 (2003) no. 1, pp. 28-33.

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

In the article, we establish the projectivity property for the enriched Galois groups of multi-valued fields having a near Boolean family of valuation rings and satisfying the arithmetic local-global principle $\mathrm{LG}_A$. This property extends the corresponding property that was proved by the author for the case of Boolean families. As application, we give a sufficient condition for the inverse Galois problem to be solvable. This condition can be applied in particular to the wonderful extensions of the field of rational numbers. 
@article{MT_2003_6_1_a1,
     author = {Yu. L. Ershov},
     title = {Projectivity of {the~Absolute} {Galois} {Groups} of {Multi-Valued} {Fields}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {28--33},
     publisher = {mathdoc},
     volume = {6},
     number = {1},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2003_6_1_a1/}
}
TY  - JOUR
AU  - Yu. L. Ershov
TI  - Projectivity of the~Absolute Galois Groups of Multi-Valued Fields
JO  - Matematičeskie trudy
PY  - 2003
SP  - 28
EP  - 33
VL  - 6
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2003_6_1_a1/
LA  - ru
ID  - MT_2003_6_1_a1
ER  - 
%0 Journal Article
%A Yu. L. Ershov
%T Projectivity of the~Absolute Galois Groups of Multi-Valued Fields
%J Matematičeskie trudy
%D 2003
%P 28-33
%V 6
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2003_6_1_a1/
%G ru
%F MT_2003_6_1_a1
Yu. L. Ershov. Projectivity of the~Absolute Galois Groups of Multi-Valued Fields. Matematičeskie trudy, Tome 6 (2003) no. 1, pp. 28-33. http://geodesic.mathdoc.fr/item/MT_2003_6_1_a1/

[1] Ershov Yu. L., “Polya s nepreryvnymi lokalnymi elementarnymi svoistvami. II”, Algebra i logika, 34:3 (1995), 262–273 | MR | Zbl

[2] Ershov Yu. L., “Svobodnye $\Delta^*$-gruppy”, Algebra i logika, 35:2 (1996), 154–172 | MR | Zbl

[3] Ershov Yu. L., Kratno normirovannye polya, Nauchnaya kniga, Novosibirsk, 2000

[4] Ershov Yu. L., “Ob udivitelnykh rasshireniyakh polya ratsionalnykh chisel”, Dokl. RAN, 373:1 (2000), 15–16 | MR | Zbl

[5] Ershov Yu. L., “Neposredstvennye rasshireniya pryuferovykh kolets”, Algebra i logika, 40:3 (2001), 262–289 | MR | Zbl

[6] Ershov Yu. L., “Projectivity of absolute Galois groups of $RC_\zeta^*$-fields”, Algebra, Proc. III Int. Alg. Conf. (Krasnoyarsk), eds. Yu. L. Ershov et al., Walter de Gruyter, Berlin; New York, 1996, 63–80 | MR | Zbl