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, p. 831-848

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 = {Virdol, Cristian},
     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},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 19},
     number = {3-4},
     year = {2010},
     pages = {831-848},
     doi = {10.5802/afst.1267},
     mrnumber = {2790819},
     zbl = {1214.11077},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2010_6_19_3-4_831_0}
}
Virdol, Cristian. 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. http://www.numdam.org/item/AFST_2010_6_19_3-4_831_0/

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