Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 233-259
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A. N. Zinoviev. Generalized Artin–Hasse and Iwasawa formulas for the Hilbert symbol in a higher local field. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 9, Tome 289 (2002), pp. 233-259. http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a12/
@article{ZNSL_2002_289_a12,
author = {A. N. Zinoviev},
title = {Generalized {Artin{\textendash}Hasse} and {Iwasawa} formulas for the {Hilbert} symbol in a higher local field},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {233--259},
year = {2002},
volume = {289},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a12/}
}
TY - JOUR
AU - A. N. Zinoviev
TI - Generalized Artin–Hasse and Iwasawa formulas for the Hilbert symbol in a higher local field
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2002
SP - 233
EP - 259
VL - 289
UR - http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a12/
LA - ru
ID - ZNSL_2002_289_a12
ER -
%0 Journal Article
%A A. N. Zinoviev
%T Generalized Artin–Hasse and Iwasawa formulas for the Hilbert symbol in a higher local field
%J Zapiski Nauchnykh Seminarov POMI
%D 2002
%P 233-259
%V 289
%U http://geodesic.mathdoc.fr/item/ZNSL_2002_289_a12/
%G ru
%F ZNSL_2002_289_a12
In the paper we consider the generalized Hilbert symbol in the cyclotomic extension of an absolutely unramified higher local field of characteristic 0 with perfect last residue field of characteristic $p>2$. We deduce the generalized Artin–Hasse and Iwasawa formulas from the explicit Kummer type Vostokov formula.
