Base change for Bernstein centers of depth zero principal series blocks

Haines, Thomas J.

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 45 (2012) no. 5, pp. 681-718.

Soit $G$ un groupe non-ramifié sur un corps $p$-adique. On définit un homomorphisme de changement de base pour les centres de Bernstein des blocs des séries principales de niveau zéro, et on démontre le lemme fondamental correspondant. Ce résultat est utilisé dans le calcul du facteur local en $p$ des variétés de Shimura à structure de niveau ${\Gamma }_1\left(p\right)$ dans l’article avec M. Rapoport [15] publié en tandem avec cet article dans ce même journal.

Let $G$ be an unramified group over a $p$-adic field. This article introduces a base change homomorphism for Bernstein centers of depth-zero principal series blocks for $G$ and proves the corresponding base change fundamental lemma. This result is used in the approach to Shimura varieties with ${\Gamma }_1\left(p\right)$-level structure initiated by M. Rapoport and the author in [15].

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