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 -adic sheaves) of the global Schubert varieties, which are the equal characteristic counterparts of the local models. ContentsXINWEN ZHU 6.2.Reduction of Theorem 3.9 to Theorem 6.8 42 6.3.Special parahorics 48 6.4.Proof of Theorem 6.8 54 7. Proofs II: the nearby cycles 59 7.1.The strategy 59 7.2.Central sheaves 60 7.3.Wakimoto filtrations 64 7.4.Proof of Theorem 3.8 68 8. Appendix I: line bundles on the local models for ramified unitary groups 69 9. Appendix II: Some recollections and proofs 76 9.1.Combinatorics of Iwahori-Weyl group 76 9.2.Deformation to the normal cone 78 9.3.Frobenius morphisms 79 References 81