In this paper we prove some non-solvable base change for Hilbert modular representations, and we use this result to show the meromorphic continuation to the entire complex plane of the zeta functions of some twisted quaternionic Shimura varieties. The zeta functions of the twisted quaternionic Shimura varieties are computed at all places.
Dans cet article, nous montrons un changement de base non-résoluble pour certaines représentations modulaires de Hilbert et nous utilisons ce résultat pour établir le prolongement méromorphe à tout le plan complexe des fonctions zêta de certaines variétés de Shimura quaternioniques tordues. Les fonctions zêta des variétés de Shimura quaternioniques tordues sont calculées à toutes les places.
@article{AFST_2010_6_19_3-4_831_0,
author = {Cristian Virdol},
title = {Non-solvable base change for {Hilbert} modular representations and zeta functions of twisted quaternionic {Shimura} varieties},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {831--848},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 19},
number = {3-4},
year = {2010},
doi = {10.5802/afst.1267},
mrnumber = {2790819},
zbl = {1214.11077},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1267/}
}
TY - JOUR AU - Cristian Virdol TI - Non-solvable base change for Hilbert modular representations and zeta functions of twisted quaternionic Shimura varieties JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2010 SP - 831 EP - 848 VL - 19 IS - 3-4 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1267/ DO - 10.5802/afst.1267 LA - en ID - AFST_2010_6_19_3-4_831_0 ER -
%0 Journal Article %A Cristian Virdol %T Non-solvable base change for Hilbert modular representations and zeta functions of twisted quaternionic Shimura varieties %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2010 %P 831-848 %V 19 %N 3-4 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1267/ %R 10.5802/afst.1267 %G en %F AFST_2010_6_19_3-4_831_0
Cristian Virdol. Non-solvable base change for Hilbert modular representations and zeta functions of twisted quaternionic Shimura varieties. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 19 (2010) no. 3-4, pp. 831-848. doi : 10.5802/afst.1267. https://afst.centre-mersenne.org/articles/10.5802/afst.1267/
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