Sur une conjecture de Kottwitz au bord

TL;DR

This paper investigates the intersection cohomology of Siegel modular varieties' minimal compactification at bad reduction places, computing Frobenius traces on nearby cycles, generalizing prior results by Morel, Haines, and Ngo.

Contribution

It provides a new computation of Frobenius traces on intersection cohomology, extending previous work to more general settings.

Findings

Computed semi-simple trace of Frobenius on nearby cycles

Unified results of Morel, Haines, and Ngo in a broader context

Enhanced understanding of bad reduction in Siegel modular varieties

Abstract

We are interested in the intersection cohomology of the minimal compactification of Siegel modular varieties at some places of bad reduction. We compute the semi-simple trace of the Frobenius morphism on the fibers of the nearby cycles of the intersection complex. We obtain a common generalization of results of Morel and Haines and Ngo.