Twisted eigenvarieties and self-dual representations
Annales de l'Institut Fourier, Volume 68 (2018) no. 6, pp. 2381-2444.

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.

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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3212
Classification: 11F33,  11F55,  11F75,  11F85
Keywords: eigenvariety, p-adic automorphic form, self-dual representation
Xiang, Zhengyu 1

1 SCMS and Fudan University East Guanghua Main Tower, Room 2214 220 Handan Road, Shanghai 200433 (P.R.C.)
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Xiang, Zhengyu. Twisted eigenvarieties and self-dual representations. Annales de l'Institut Fourier, Volume 68 (2018) no. 6, pp. 2381-2444. doi : 10.5802/aif.3212. https://aif.centre-mersenne.org/articles/10.5802/aif.3212/

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