Geodesic
On Inaba extensions for two-dimensional local fields of mixed characteristic
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 38, Tome 513 (2022), pp. 57-73
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The paper is devoted to extensions of higher local fields determined by certain matrix equations introduced by E. Inaba. It is proved that any extension decomposable into a tower of Artin–Schreier extensions can be embedded into an Inaba extension that is a composite of the given extension and another Inaba extension. Next, any $p$-extension with elementary Abelian Galois group can be embedded into an extension with the Galois group isomorphic to a group of unipotent matrices over the field with $p$ elements. 
@article{ZNSL_2022_513_a4,
     author = {I. B. Zhukov and O. Yu. Ivanova},
     title = {On {Inaba} extensions for two-dimensional local fields of mixed characteristic},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {57--73},
     year = {2022},
     volume = {513},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_513_a4/}
}
TY  - JOUR
AU  - I. B. Zhukov
AU  - O. Yu. Ivanova
TI  - On Inaba extensions for two-dimensional local fields of mixed characteristic
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2022
SP  - 57
EP  - 73
VL  - 513
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2022_513_a4/
LA  - ru
ID  - ZNSL_2022_513_a4
ER  - 
%0 Journal Article
%A I. B. Zhukov
%A O. Yu. Ivanova
%T On Inaba extensions for two-dimensional local fields of mixed characteristic
%J Zapiski Nauchnykh Seminarov POMI
%D 2022
%P 57-73
%V 513
%U http://geodesic.mathdoc.fr/item/ZNSL_2022_513_a4/
%G ru
%F ZNSL_2022_513_a4
I. B. Zhukov; O. Yu. Ivanova. On Inaba extensions for two-dimensional local fields of mixed characteristic. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 38, Tome 513 (2022), pp. 57-73. http://geodesic.mathdoc.fr/item/ZNSL_2022_513_a4/

[1] E. Inaba, “On matrix equations for Galois extensions of fields with characteristic $p$”, Natur. Sci. Rep. Ochanomizu Univ., 12 (1961), 26–36 | MR

[2] S. V. Vostokov, I. B. Zhukov, O. Yu. Ivanova, “Rasshireniya Inaby polnykh polei kharakteristiki $0$”, Chebyshevskii sbornik, 20:3 (2019), 124–133 | MR

[3] O. Yu. Ivanova, “Zadanie svirepogo tsiklicheskogo rasshireniya uravneniem Inaby”, Zap. nauchn. semin. POMI, 513, 2022, 74–84

[4] I. B. Fesenko, S. V. Vostokov, Local fields and their extensions. A constructive approach, Second edition, AMS, Providence, RI, 2002 | MR