On the coherence conjecture of Pappas and Rapoport

Abstract

We prove the (generalized) coherence conjecture proposed by Pappas and Rapoport. As a corollary, one of their theorems, 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 equal characteristic counterparts of the local models.