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arXiv · 1512.01149

Integral models of Shimura varieties with parahoric level structure

M. Kisin·G. Pappas
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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.

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M. Kisin, G. Pappas. 2018-04-12. Integral models of Shimura varieties with parahoric level structure. https://arxiv.org/abs/1512.01149

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