Local models for Weil-restricted groups. (27th September 2016)

• Record Type: Journal Article
• Authors: Levin, Brandon
• Is Part Of: Compositio mathematica. Volume 152:Number 12(2016)
• Page Start: 2563
• Page End: 2601
• Publication Date: 2016-09-27
• Subjects: 14G35 (primary), -- 11G18, -- 14M15 (secondary); algebraic groups, -- affine Grassmannians, -- nearby cycles, -- Shimura varieties; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X1600765X
• Languages: English
• ISSNs: 0010-437X

Abstract

Abstract : We extend the group-theoretic construction of local models of Pappas and Zhu [ Local models of Shimura varieties and a conjecture of Kottwitz, Invent. Math.194 (2013), 147–254] to the case of groups obtained by Weil restriction along a possibly wildly ramified extension. This completes the construction of local models for all reductive groups when $p\geqslant 5$ . We show that the local models are normal with special fiber reduced and study the monodromy action on the sheaves of nearby cycles. As a consequence, we prove a conjecture of Kottwitz that the semi-simple trace of Frobenius gives a central function in the parahoric Hecke algebra. We also introduce a notion of splitting model and use this to study the inertial action in the case of an unramified group.