Integral models of Shimura varieties with parahoric level structure

2015/12/03 by Mark Kisin, Kisin, M., G. Pappas +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1512.01149

openalex publication_date 2015/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an odd prime p, 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 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.

Citations

• A guide to the reduction modulo p of Shimura varieties

Cited by

• Dual Shellability of Admissible Set and Cohen-Macaulayness of Local Models

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