Integral models of Shimura varieties with parahoric level structure

By M. Kisin, Georgios Pappas. Publications mathématiques (Bures-sur-Yvette), 2015

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For a prime p>2$p > 2$, we construct integral models over p$p$ for Shimura varieties with parahoric level structure, attached to Shimura data (G,X)$(G,X)$ of abelian type, such that G$G$ splits over a tamely ramified extension of Qp${\mathbf {Q}}_{\,p}$. 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.

Subfields: Geometry and Topology, Mathematical Physics

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