Local models for Weil-restricted groups

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10 Scopus citations

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 ≥ 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.

Original languageEnglish (US)
Pages (from-to)2563-2601
Number of pages39
JournalCompositio Mathematica
Volume152
Issue number12
DOIs
StatePublished - Dec 1 2016
Externally publishedYes

Keywords

  • affine Grassmannians
  • algebraic groups
  • nearby cycles
  • Shimura varieties

ASJC Scopus subject areas

  • Algebra and Number Theory

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