An explicit formula for the Hilbert symbol of a formal group

Floric Tavares Ribeiro[1]

  • [1] Université de Franche-Comté Département de Mathématiques 16 route de Gray 25000 Besançon (France)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 1, page 261-318
  • ISSN: 0373-0956

Abstract

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A Brückner-Vostokov formula for the Hilbert symbol of a formal group was established by Abrashkin under the assumption that roots of unity belong to the base field. The main motivation of this work is to remove this hypothesis. It is obtained by combining methods of ( ϕ , Γ )-modules and a cohomological interpretation of Abrashkin’s technique. To do this, we build ( ϕ , Γ )-modules adapted to the false Tate curve extension and generalize some related tools like the Herr complex with explicit formulas for the cup-product and the Kummer map.

How to cite

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Tavares Ribeiro, Floric. "An explicit formula for the Hilbert symbol of a formal group." Annales de l’institut Fourier 61.1 (2011): 261-318. <http://eudml.org/doc/219753>.

@article{TavaresRibeiro2011,
abstract = {A Brückner-Vostokov formula for the Hilbert symbol of a formal group was established by Abrashkin under the assumption that roots of unity belong to the base field. The main motivation of this work is to remove this hypothesis. It is obtained by combining methods of ($\varphi , \Gamma $)-modules and a cohomological interpretation of Abrashkin’s technique. To do this, we build ($\varphi , \Gamma $)-modules adapted to the false Tate curve extension and generalize some related tools like the Herr complex with explicit formulas for the cup-product and the Kummer map.},
affiliation = {Université de Franche-Comté Département de Mathématiques 16 route de Gray 25000 Besançon (France)},
author = {Tavares Ribeiro, Floric},
journal = {Annales de l’institut Fourier},
keywords = {$p$-adic representations; ($\phi ,\Gamma $)-modules; formal groups; explicit reciprocity law; -adic representations; -modules},
language = {eng},
number = {1},
pages = {261-318},
publisher = {Association des Annales de l’institut Fourier},
title = {An explicit formula for the Hilbert symbol of a formal group},
url = {http://eudml.org/doc/219753},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Tavares Ribeiro, Floric
TI - An explicit formula for the Hilbert symbol of a formal group
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 1
SP - 261
EP - 318
AB - A Brückner-Vostokov formula for the Hilbert symbol of a formal group was established by Abrashkin under the assumption that roots of unity belong to the base field. The main motivation of this work is to remove this hypothesis. It is obtained by combining methods of ($\varphi , \Gamma $)-modules and a cohomological interpretation of Abrashkin’s technique. To do this, we build ($\varphi , \Gamma $)-modules adapted to the false Tate curve extension and generalize some related tools like the Herr complex with explicit formulas for the cup-product and the Kummer map.
LA - eng
KW - $p$-adic representations; ($\phi ,\Gamma $)-modules; formal groups; explicit reciprocity law; -adic representations; -modules
UR - http://eudml.org/doc/219753
ER -

References

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