Class formulae for real abelian fields

Jean-Robert Belliard[1]; Thong Nguyen Quang Do[1]

  • [1] Université de Franche-Comté, Laboratoire de Mathématiques, CNRS UMR 6623, 16 route de Gray, 25030 Besançon Cedex (France)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 4, page 903-937
  • ISSN: 0373-0956

Abstract

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We show p -adic and “character by character” refinements of Sinnott’s index formula for a totally real abelian number field. Such refinements have also been obtained by Kuz’min by different methods (but see comments in the introduction). Applications are given to Iwasawa theory of semi-local units and cyclotomic units.

How to cite

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Belliard, Jean-Robert, and Nguyen Quang Do, Thong. "Formules de classes pour les corps abéliens réels." Annales de l’institut Fourier 51.4 (2001): 903-937. <http://eudml.org/doc/115940>.

@article{Belliard2001,
abstract = {Nous montrons des raffinements $p$-adique et “caractères par caractères” de la formule d’indice de Sinnott pour un corps abélien totalement réel. De tels raffinements ont aussi été obtenus par Kuz’min avec des méthodes différentes (voir les commentaires en introduction). Nous donnons des applications à la théorie d’Iwasawa des unités semi- locales et cyclotomiques.},
affiliation = {Université de Franche-Comté, Laboratoire de Mathématiques, CNRS UMR 6623, 16 route de Gray, 25030 Besançon Cedex (France); Université de Franche-Comté, Laboratoire de Mathématiques, CNRS UMR 6623, 16 route de Gray, 25030 Besançon Cedex (France)},
author = {Belliard, Jean-Robert, Nguyen Quang Do, Thong},
journal = {Annales de l’institut Fourier},
keywords = {class groups; $p$-adic $L$ functions; Iwasawa’s theory},
language = {fre},
number = {4},
pages = {903-937},
publisher = {Association des Annales de l'Institut Fourier},
title = {Formules de classes pour les corps abéliens réels},
url = {http://eudml.org/doc/115940},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Belliard, Jean-Robert
AU - Nguyen Quang Do, Thong
TI - Formules de classes pour les corps abéliens réels
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 4
SP - 903
EP - 937
AB - Nous montrons des raffinements $p$-adique et “caractères par caractères” de la formule d’indice de Sinnott pour un corps abélien totalement réel. De tels raffinements ont aussi été obtenus par Kuz’min avec des méthodes différentes (voir les commentaires en introduction). Nous donnons des applications à la théorie d’Iwasawa des unités semi- locales et cyclotomiques.
LA - fre
KW - class groups; $p$-adic $L$ functions; Iwasawa’s theory
UR - http://eudml.org/doc/115940
ER -

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