Twisted eigenvarieties and self-dual representations

Xiang, Zhengyu

Annales de l'Institut Fourier, Tome 68 (2018) no. 6, pp. 2381-2444.

Pour un groupe réductif $G$ et un automorphisme d’ordre fini $\iota$ de type Cartan de $G$ nous construisons une variété propre paramétrant les systèmes propres de Hecke automorphes cuspidaux $\iota$-invariants de $G$. En particulier, pour $G=G{l}_n$, 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 $\iota$ of $G$, we construct an eigenvariety parameterizing $\iota$-invariant cuspidal Hecke eigensystems of $G$. In particular, for $G=G{l}_n$, 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.

Classification : 11F33, 11F55, 11F75, 11F85
Keywords: eigenvariety, p-adic automorphic form, self-dual representation
Mot clés : variété propre, forme automorphe p-adique, représentation autoduale

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