Geodesic
Norm series in multidimensional local fields
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 10, Tome 305 (2003), pp. 60-83 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In the present paper, the notion of norm series with respect to the norm residue symbol is generalized to a multidimensional local field. Necessary and sufficient conditions for the existence of norm series are obtained. 
@article{ZNSL_2003_305_a3,
     author = {S. V. Vostokov and G. K. Pak},
     title = {Norm series in multidimensional local fields},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {60--83},
     year = {2003},
     volume = {305},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_305_a3/}
}
TY  - JOUR
AU  - S. V. Vostokov
AU  - G. K. Pak
TI  - Norm series in multidimensional local fields
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2003
SP  - 60
EP  - 83
VL  - 305
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2003_305_a3/
LA  - ru
ID  - ZNSL_2003_305_a3
ER  - 
%0 Journal Article
%A S. V. Vostokov
%A G. K. Pak
%T Norm series in multidimensional local fields
%J Zapiski Nauchnykh Seminarov POMI
%D 2003
%P 60-83
%V 305
%U http://geodesic.mathdoc.fr/item/ZNSL_2003_305_a3/
%G ru
%F ZNSL_2003_305_a3
S. V. Vostokov; G. K. Pak. Norm series in multidimensional local fields. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 10, Tome 305 (2003), pp. 60-83. http://geodesic.mathdoc.fr/item/ZNSL_2003_305_a3/

[1] S. V. Vostokov, R. Perlis, “Normennye ryady dlya formalnykh grupp Lyubina–Teita”, Zap. nauchn. semin. POMI, 281, 2001, 105–127 | MR | Zbl

[2] S. V. Vostokov, “Yavnaya konstruktsiya teorii polei klassov dlya mnogomernykh lokalnykh polei”, Izv. AN SSSR. Ser. matem, 49:2 (1985), 283–308 | MR

[3] S. V. Vostokov, I. B. Zhukov, I. B. Fesenko, “K teorii mnogomernykh lokalnykh polei. Metody i konstruktsii”, Algebra i analiz, 2:4 (1990), 91–118 | MR | Zbl

[4] F. Lorenz, S. Vostokov, “Honda Groups and Explicit Pairings on the Modules of Cartier Curves”, Contemporary Mathematics, 300 (2002), 143–170 | MR | Zbl

[5] K. Kato, “A generalization of local class field theory by using K-groups, I, II”, J. Fac. Sci. Univ. Tokyo, Sect. IA, 26 (1979), 303–376 ; J. Fac. Sci. Univ. Tokyo, Sect. IA, 27 (1980), 603–683 | MR | Zbl | MR | Zbl

[6] A. N. Parshin, “Polya klassov i algebraicheskaya $K$-teoriya”, UMN, 30:1 (1975), 253–254 | MR | Zbl

[7] A. N. Parshin, “Lokalnaya teoriya polei klassov”, Trudy MIAN SSSR, 165, 1984, 143–170 | MR | Zbl

[8] T. B. Belyaeva, S. V. Vostokov, “Simvol Gilberta v polnom mnogomernom pole, I”, Zap. nauchn. semin. POMI, 281, 2001, 5–34 | MR | Zbl

[9] A. I. Madunts, “O skhodimosti ryadov nad lokalnymi polyami”, Zap. nauchn. semin. LOMI, 198, 1991, 28–30 | MR | Zbl

[10] S. V. Vostokov, “Yavnaya forma zakona vzaimnosti”, Izv. AN SSSR. Ser. matem., 42:6 (1978), 1288–1321 | MR | Zbl

[11] G. Henniart, “Sur les lois de reciprocité explicites, I”, J. Reine und Angew. Math., 329 (1981), 172–203 | MR

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