Vertexwise criteria for admissibility of alcoves

Abstract

We give a new description of the set $Adm(\mu )$ of admissible alcoves as an intersection of certain "obtuse cones" of alcoves, and we show this description may be given by imposing conditions vertexwise. We use this to prove the vertexwise admissibility conjecture of Pappas-Rapoport-Smithling. The same idea gives simple proofs of two ingredients used in the proof of the Kottwitz-Rapoport conjecture on existence of crystals with additional structure.

14 pages. This article appeared in the American Journal of Mathematics, Volume 139, Number 3, June 2017, pages 769-784, ©2017, Johns Hopkins University Press

References in corpus (3)

• A guide to the reduction modulo p of Shimura varieties
• On parahoric subgroups
• Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties

Cited by in corpus (2)

• Hecke algebras and $p$-adic groups
• Stratifications in the reduction of Shimura varieties