Geodesic
On the Fixed Field of a Generic Automorphism
Matematičeskie trudy, Tome 4 (2001) no. 1, pp. 25-35 
K. Zh. Kudaibergenov. On the Fixed Field of a Generic Automorphism. Matematičeskie trudy, Tome 4 (2001) no. 1, pp. 25-35. http://geodesic.mathdoc.fr/item/MT_2001_4_1_a2/
@article{MT_2001_4_1_a2,
     author = {K. Zh. Kudaibergenov},
     title = {On {the~Fixed} {Field} of {a~Generic} {Automorphism}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {25--35},
     year = {2001},
     volume = {4},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2001_4_1_a2/}
}
TY  - JOUR
AU  - K. Zh. Kudaibergenov
TI  - On the Fixed Field of a Generic Automorphism
JO  - Matematičeskie trudy
PY  - 2001
SP  - 25
EP  - 35
VL  - 4
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MT_2001_4_1_a2/
LA  - ru
ID  - MT_2001_4_1_a2
ER  - 
%0 Journal Article
%A K. Zh. Kudaibergenov
%T On the Fixed Field of a Generic Automorphism
%J Matematičeskie trudy
%D 2001
%P 25-35
%V 4
%N 1
%U http://geodesic.mathdoc.fr/item/MT_2001_4_1_a2/
%G ru
%F MT_2001_4_1_a2

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

The notion of an almost generic automorphism is introduced and the fixed field is studied of an almost generic automorphism of a stable field. In particular, it is proven that the fixed field of an almost generic automorphism of a separably closed field is regularly closed and its absolute Galois group is isomorphic to $\widehat{\mathbb Z}$.

[1] Gryunberg K., “Prokonechnye gruppy”, Algebraicheskaya teoriya chisel, Mir, M., 1969

[2] Ershov Yu. L., “Polya s razreshimoi teoriei”, Dokl. AN SSSR, 251:1 (1967), 19–20

[3] Ershov Yu. L., “Algoritmicheskie problemy v teorii polei”, Spravochnaya kniga po matematicheskoi logike, Chast III: Dopolnenie, Nauka, M., 1982, 269–353

[4] Leng S., Algebra, Mir, M., 1968

[5] Lascar D., “Les beaux automorphismes”, Arch. Math. Logic, 31:1 (1991), 55–68 | DOI | MR | Zbl

[6] Macintyre A., “Generic automorphisms of fields”, Ann. Pure Appl. Logic, 88:2–3 (1997), 165–180 | DOI | MR | Zbl

[7] Poizat B., Groupes Stables, Villeurbanne, Paris, 1987 | MR | Zbl

[8] Shelah S., Classification Theory and the Number of Nonisomorphic Models, North-Holland, Amsterdam, 1978 | MR | Zbl