Geodesic
Lubin–Tate formal module in a cyclic unramified $p$-extension as Galois module
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 27, Tome 430 (2014), pp. 61-66 
S. V. Vostokov; I. I. Nekrasov. Lubin–Tate formal module in a cyclic unramified $p$-extension as Galois module. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 27, Tome 430 (2014), pp. 61-66. http://geodesic.mathdoc.fr/item/ZNSL_2014_430_a5/
@article{ZNSL_2014_430_a5,
     author = {S. V. Vostokov and I. I. Nekrasov},
     title = {Lubin{\textendash}Tate formal module in a~cyclic unramified $p$-extension as {Galois} module},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {61--66},
     year = {2014},
     volume = {430},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_430_a5/}
}
TY  - JOUR
AU  - S. V. Vostokov
AU  - I. I. Nekrasov
TI  - Lubin–Tate formal module in a cyclic unramified $p$-extension as Galois module
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2014
SP  - 61
EP  - 66
VL  - 430
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2014_430_a5/
LA  - ru
ID  - ZNSL_2014_430_a5
ER  - 
%0 Journal Article
%A S. V. Vostokov
%A I. I. Nekrasov
%T Lubin–Tate formal module in a cyclic unramified $p$-extension as Galois module
%J Zapiski Nauchnykh Seminarov POMI
%D 2014
%P 61-66
%V 430
%U http://geodesic.mathdoc.fr/item/ZNSL_2014_430_a5/
%G ru
%F ZNSL_2014_430_a5

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In this paper we describe the structure of the $\mathcal O_K[G]$-module $F(\mathfrak m_M)$, where $M/L$, $L/K$, $K/\mathbb Q_p$ are finite Galois extensions ($p$ is fixed prime number), $G=\mathrm{Gal}(M/L)$, $\mathfrak m_M$ is a maximal ideal of $M$ and $F$ is a formal Lubin–Tate group law over $\mathcal O_K$ for a prime element $\pi$.

[1] K. Iwasawa, “On Galois groups of local fields”, Trans. Amer. Soc., 80:2 (1955), 448–469 | DOI | MR | Zbl

[2] K. Iwasawa, “On local cyclotomic fields”, J. Math. Soc. Japan, 12:1 (1960), 16–21 | DOI | MR | Zbl

[3] M. Krasner, “Sur la représentation exponentielle dans les corps relativement galoisiens de nombres $p$-adiques”, Acta arithm., 3 (1939), 133–173 | Zbl

[4] Dzh. Kassels, A. Frëlikh (red.), Algebraicheskaya teoriya chisel, Mir, M., 1969 | MR

[5] Z. I. Borevich, “Multiplikativnaya gruppa regulyarnogo lokalnogo polya s tsiklicheskoi gruppoi operatorov”, Izv. AN SSSR, ser. matem., 24:2 (1960), 145–152 | MR | Zbl

[6] Z. I. Borevich, “O multiplikativnoi gruppe tsiklicheskikh $p$-rasshirenii lokalnogo polya”, Tr. MIAN SSSR, 80, 1965, 16–29 | MR | Zbl

[7] Z. I. Borevich, S. V. Vostokov, “Koltso tselykh elementov rasshireniya prostoi stepeni lokalnogo polya kak modul Galua”, Zap. nauchn. semin. LOMI, 31, 1973, 24–37 | MR | Zbl

[8] S. V. Vostokov, “Idealy abeleva $p$-rasshireniya lokalnogo polya kak moduli Galua”, Zap. nauchn. semin. LOMI, 57, 1976, 64–84 | MR | Zbl

[9] V. A. Kolyvagin, “Formalnye gruppy i simvol normennogo vycheta”, Izv. AN SSSR, Ser. matem., 43:5 (1979), 1054–1120 | MR | Zbl