Geodesic
The Shafarevich basis in higher dimensional local fields
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 24, Tome 413 (2013), pp. 115-133 
E. V. Ikonnikova; E. V. Shaverdova. The Shafarevich basis in higher dimensional local fields. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 24, Tome 413 (2013), pp. 115-133. http://geodesic.mathdoc.fr/item/ZNSL_2013_413_a5/
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     title = {The {Shafarevich} basis in higher dimensional local fields},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_413_a5/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

This paper presents a generalization of Shafarevich basis for $n$-dimensional local fields with perfect last residue field. We consider the group of principal units of such fields and construct its multiplicative basis.

[1] S. V. Vostokov, “Yavnaya konstruktsiya teorii polei klassov mnogomernogo lokalnogo polya”, Izv. AN SSSR. Ser. matem., 49:2 (1985), 283–308 | MR | Zbl

[2] S. V. Vostokov, “Sparivanie na $K$-gruppakh mnogomernykh polnykh polei”, Trudy S.-Peterburg. matem. obschestva, 3, 1994, 140–184 | MR

[3] I. B. Zhukov, A. I. Madunts, “Additivnye i multiplikativnye razlozheniya v mnogomernykh lokalnykh polyakh”, Zap. nauchn. semin. POMI, 272, 2000, 186–196 | MR | Zbl

[4] A. I. Madunts, Skhodimost posledovatelnostei i ryadov v mnogomernykh polnykh polyakh, Kandidatskaya dissertatsiya, SPbGU, 1995

[5] S. V. Vostokov, “Kanonicheskii bazis Genzelya–Shafarevicha v polnykh diskretno-normirovannykh polyakh”, Zap. nauchn. semin. POMI, 394, 2011, 174–193 | MR

[6] I. B. Fesenko, S. V. Vostokov, Local fields and their extensions, AMS Bookstore, 2002 | MR | Zbl

[7] I. R. Shafarevich, “Obschii zakon vzaimnosti”, Matem. sb., 26(68):1 (1950), 113–146 | MR | Zbl