Trace of Frobenius on nearby cycles for a $Γ_1(p)$-local model

Abstract

We compute the trace of Frobenius on the sheaf of nearby cycles for the integral model of the Siegel modular variety with pro-p Iwahori level structure, constructed by Haines and Stroh, in the case of $\text{GSp}_4$. To this end, we make use of a semistable resolution of this model due to Shadrach. Finally, we compare our results with calculations made by Horn, confirming a conjecture of Haines and Kottwitz in this case.