The field-of-norms functor and the Hilbert symbol for higher local fields

Victor Abrashkin[1]; Ruth Jenni

  • [1] Department of Mathematical Sciences Durham University Science Laboratories South Rd, Durham DH1 3LE United Kingdom

Journal de Théorie des Nombres de Bordeaux (2012)

  • Volume: 24, Issue: 1, page 1-39
  • ISSN: 1246-7405

Abstract

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The field-of-norms functor is applied to deduce an explicit formula for the Hilbert symbol in the mixed characteristic case from the explicit formula for the Witt symbol in characteristic p > 2 in the context of higher local fields. Is is shown that a “very special case” of this construction gives Vostokov’s explicit formula.

How to cite

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Abrashkin, Victor, and Jenni, Ruth. "The field-of-norms functor and the Hilbert symbol for higher local fields." Journal de Théorie des Nombres de Bordeaux 24.1 (2012): 1-39. <http://eudml.org/doc/251132>.

@article{Abrashkin2012,
abstract = {The field-of-norms functor is applied to deduce an explicit formula for the Hilbert symbol in the mixed characteristic case from the explicit formula for the Witt symbol in characteristic $p&gt;2$ in the context of higher local fields. Is is shown that a “very special case” of this construction gives Vostokov’s explicit formula.},
affiliation = {Department of Mathematical Sciences Durham University Science Laboratories South Rd, Durham DH1 3LE United Kingdom},
author = {Abrashkin, Victor, Jenni, Ruth},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {higher local fields; field-of-norms; Hilbert Symbol; Vostokov’s pairing; higher local symbols; Hilbert symbol; fields of norms; Vostokov's pairing},
language = {eng},
month = {3},
number = {1},
pages = {1-39},
publisher = {Société Arithmétique de Bordeaux},
title = {The field-of-norms functor and the Hilbert symbol for higher local fields},
url = {http://eudml.org/doc/251132},
volume = {24},
year = {2012},
}

TY - JOUR
AU - Abrashkin, Victor
AU - Jenni, Ruth
TI - The field-of-norms functor and the Hilbert symbol for higher local fields
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2012/3//
PB - Société Arithmétique de Bordeaux
VL - 24
IS - 1
SP - 1
EP - 39
AB - The field-of-norms functor is applied to deduce an explicit formula for the Hilbert symbol in the mixed characteristic case from the explicit formula for the Witt symbol in characteristic $p&gt;2$ in the context of higher local fields. Is is shown that a “very special case” of this construction gives Vostokov’s explicit formula.
LA - eng
KW - higher local fields; field-of-norms; Hilbert Symbol; Vostokov’s pairing; higher local symbols; Hilbert symbol; fields of norms; Vostokov's pairing
UR - http://eudml.org/doc/251132
ER -

References

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  8. J.-M.Fontaine, Representations p -adiques des corps locaux (1-ere partie). In: The Grothendieck Festschrift, A Collection of Articles in Honor of the 60th Birthday of Alexander Grothendieck, vol.  II, 1990, 249–309. Zbl0743.11066MR1106901
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  22. I. Zhukov, Higher dimensional local fields. (Münster, 1999), Geom. Topol. Monogr. (2000), no.3, 5–18. Zbl1008.11057MR1804916

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