We show -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.
Nous montrons des raffinements -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.
Mot clés : groupes de classes, fonctions $L\,p$-adiques, théorie d’Iwasawa
Keywords: class groups, $p$-adic $L$ functions, Iwasawa’s theory
Belliard, Jean-Robert 1; Nguyen Quang Do, Thong 1
@article{AIF_2001__51_4_903_0, author = {Belliard, Jean-Robert and Nguyen Quang Do, Thong}, title = {Formules de classes pour les corps ab\'eliens r\'eels}, journal = {Annales de l'Institut Fourier}, pages = {903--937}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {51}, number = {4}, year = {2001}, doi = {10.5802/aif.1840}, zbl = {1007.11063}, mrnumber = {1849210}, language = {fr}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1840/} }
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 SP - 903 EP - 937 VL - 51 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1840/ DO - 10.5802/aif.1840 LA - fr ID - AIF_2001__51_4_903_0 ER -
%0 Journal Article %A Belliard, Jean-Robert %A Nguyen Quang Do, Thong %T Formules de classes pour les corps abéliens réels %J Annales de l'Institut Fourier %D 2001 %P 903-937 %V 51 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1840/ %R 10.5802/aif.1840 %G fr %F AIF_2001__51_4_903_0
Belliard, Jean-Robert; Nguyen Quang Do, Thong. Formules de classes pour les corps abéliens réels. Annales de l'Institut Fourier, Volume 51 (2001) no. 4, pp. 903-937. doi : 10.5802/aif.1840. https://aif.centre-mersenne.org/articles/10.5802/aif.1840/
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