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Publications mathématiques de l'IHÉS

, Volume 128, Issue 1, pp 121–218 | Cite as

Integral models of Shimura varieties with parahoric level structure

  • M. KisinEmail author
  • G. Pappas
Article

Abstract

For a prime \(p > 2\), we construct integral models over \(p\) for Shimura varieties with parahoric level structure, attached to Shimura data \((G,X)\) of abelian type, such that \(G\) splits over a tamely ramified extension of \({\mathbf {Q}}_{\,p}\). The local structure of these integral models is related to certain “local models”, which are defined group theoretically. Under some additional assumptions, we show that these integral models satisfy a conjecture of Kottwitz which gives an explicit description for the trace of Frobenius action on their sheaf of nearby cycles.

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© IHES and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dept. of MathematicsHarvard UniversityCambridgeUSA
  2. 2.Dept. of MathematicsMichigan State UniversityE. LansingUSA

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