We study the local factor at of the semi-simple zeta function of a Shimura variety of Drinfeld type for a level structure given at by the pro-unipotent radical of an Iwahori subgroup. Our method is an adaptation to this case of the Langlands-Kottwitz counting method. We explicitly determine the corresponding test functions in suitable Hecke algebras, and show their centrality by determining their images under the Hecke algebra isomorphisms of Goldstein, Morris, and Roche.
On étudie le facteur local en de la fonction zêta semi-simple d’une variété de Shimura du type de Drinfeld, où la structure de niveau en est donnée par le radical pro-unipotent d’un sous-groupe d’Iwahori. La méthode suivie est une adaptation à ce cas de la méthode de comptage de Langlands-Kottwitz. On détermine de façon explicite la fonction test dans l’algèbre de Hecke correspondante ; puis on démontre que c’est un élément central en déterminant ses images sous des isomorphismes d’algèbres de Hecke dus à Goldstein, Morris et Roche.
Keywords: Shimura varieties, Hasse-Weil zeta functions, automorphic $L$-functions
Mot clés : variétés de Shimura, fonctions zêta de Hasse-Weil, fonctions $L$ automorphes
@article{ASENS_2012_4_45_5_719_0, author = {Haines, Thomas J. and Rapoport, Michael}, title = {Shimura varieties with $\Gamma _1(p)$-level via {Hecke} algebra isomorphisms: the {Drinfeld} case}, journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure}, pages = {719--785}, publisher = {Soci\'et\'e math\'ematique de France}, volume = {Ser. 4, 45}, number = {5}, year = {2012}, doi = {10.24033/asens.2177}, mrnumber = {3053008}, language = {en}, url = {http://archive.numdam.org/articles/10.24033/asens.2177/} }
TY - JOUR AU - Haines, Thomas J. AU - Rapoport, Michael TI - Shimura varieties with $\Gamma _1(p)$-level via Hecke algebra isomorphisms: the Drinfeld case JO - Annales scientifiques de l'École Normale Supérieure PY - 2012 SP - 719 EP - 785 VL - 45 IS - 5 PB - Société mathématique de France UR - http://archive.numdam.org/articles/10.24033/asens.2177/ DO - 10.24033/asens.2177 LA - en ID - ASENS_2012_4_45_5_719_0 ER -
%0 Journal Article %A Haines, Thomas J. %A Rapoport, Michael %T Shimura varieties with $\Gamma _1(p)$-level via Hecke algebra isomorphisms: the Drinfeld case %J Annales scientifiques de l'École Normale Supérieure %D 2012 %P 719-785 %V 45 %N 5 %I Société mathématique de France %U http://archive.numdam.org/articles/10.24033/asens.2177/ %R 10.24033/asens.2177 %G en %F ASENS_2012_4_45_5_719_0
Haines, Thomas J.; Rapoport, Michael. Shimura varieties with $\Gamma _1(p)$-level via Hecke algebra isomorphisms: the Drinfeld case. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 45 (2012) no. 5, pp. 719-785. doi : 10.24033/asens.2177. http://archive.numdam.org/articles/10.24033/asens.2177/
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