Twisted eigenvarieties and self-dual representations  [ Variétés propres tordues et représentations autoduales ]
Annales de l'Institut Fourier, Tome 68 (2018) no. 6, pp. 2381-2444.

Pour un groupe réductif G et un automorphisme d’ordre fini ι de type Cartan de G nous construisons une variété propre paramétrant les systèmes propres de Hecke automorphes cuspidaux ι-invariants de G. En particulier, pour G=Gl n , on prouve que chaque système propre de Hecke cuspidale autoduale de pente finie peut être déformé dans une famille p-adique de sytèmes propres de Hecke cuspidaux autoduaux contenant un sous-ensemble Zariski-dense de points classiques.

For a reductive group G and a finite order Cartan-type automorphism ι of G, we construct an eigenvariety parameterizing ι-invariant cuspidal Hecke eigensystems of G. In particular, for G=Gl n , we prove, any self-dual cuspidal Hecke eigensystem can be deformed in a p-adic family of self-dual cuspidal Hecke eigensystems containing a Zariski dense subset of classical points.

Reçu le : 2016-03-09
Révisé le : 2017-09-08
Accepté le : 2017-12-13
Publié le : 2018-11-23
DOI : https://doi.org/10.5802/aif.3212
Classification : 11F33,  11F55,  11F75,  11F85
Mots clés: variété propre, forme automorphe p-adique, représentation autoduale
@article{AIF_2018__68_6_2381_0,
     author = {Xiang, Zhengyu},
     title = {Twisted eigenvarieties and self-dual representations},
     journal = {Annales de l'Institut Fourier},
     pages = {2381--2444},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {68},
     number = {6},
     year = {2018},
     doi = {10.5802/aif.3212},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2018__68_6_2381_0/}
}
Xiang, Zhengyu. Twisted eigenvarieties and self-dual representations. Annales de l'Institut Fourier, Tome 68 (2018) no. 6, pp. 2381-2444. doi : 10.5802/aif.3212. https://aif.centre-mersenne.org/item/AIF_2018__68_6_2381_0/

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