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On the coherence conjecture of Pappas and Rapoport

Zhu, Xinwen (2014) On the coherence conjecture of Pappas and Rapoport. Annals of Mathematics, 180 (1). pp. 1-85. ISSN 0003-486X.

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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 ℓ-adic sheaves) of the global Schubert varieties, which are the equal characteristic counterparts of the local models.

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Additional Information:Copyright © 2010 Annals of Mathematics. Received: 17 January 2011; Revised: 8 March 2013; Accepted: 24 April 2013. The author is grateful to D. Gaitsgory, G. Pappas, M. Rapoport, J.-K. Yu for useful discussions, and G. Pappas and M. Rapoport for reading an early draft of this paper. He is also extremely grateful to the referee for pointing out an enormous number of mistakes and typos in an early draft. The work of the author is supported by the NSF grant DMS-1001280/1313894.
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Subject Keywords:affine flag variety, local model, nearby cycles, Schubert variety
Issue or Number:1
Record Number:CaltechAUTHORS:20140919-152324725
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:49867
Deposited By: George Porter
Deposited On:20 Sep 2014 03:01
Last Modified:03 Oct 2019 07:17

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