On the coherence conjecture of Pappas and Rapoport

Abstract

We prove the (generalized) coherence conjecture of Pappas and Rapoport. As a corollary, one theorem of Pappas an Rapoport, which describes the geometry of the special fibers of the local models for ramified unitary groups, holds unconditionally. Our proof is based on the study of the geometry (in particular certain line bundles and $\ell$-adic sheaves) of the global Schubert varieties, which are the (generalized) equal characteristic counterparts of the local models.

65 pages, various mistakes corrected

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• A guide to the reduction modulo p of Shimura varieties
• Local models of Shimura varieties, I. Geometry and combinatorics
• The Geometric Satake Correspondence for Ramified Groups
• Gerbal Representations of Double Loop Groups
• Kloosterman sheaves for reductive groups
• Affine Demazure modules and $T$-fixed point subschemes in the affine Grassmannian

Cited by in corpus (1)

• Projected Richardson varieties and affine Schubert varieties