Trace of Frobenius on nearby cycles for a Γ₁(p)-local model

2025/09/25 by Giulio Marazza, Marazza, Giulio
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Tensor decomposition and applications #primary 11G18 #secondary 14G35

paper · pdf · doi:10.48550/arxiv.2509.21204

openalex publication_date 2025/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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 GSp₄. 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.

Citations

• On the geometry of integral models of Shimura varieties with Γ₁(p)-level structure
• A Combinatorial Formula for Test Functions with Pro-p Iwahori Level Structure
• The stable Bernstein center and test functions for Shimura varieties
• The supersingular locus in Siegel modular varieties with Iwahori level structure
• Introduction to Shimura varieties with bad reduction of parahoric type
• Nearby cycles for local models of some Shimura varieties
• On the flatness of local models for the symplectic group
• On the flatness of models of certain Shimura varieties of PEL-type

Related

• Nearby cycles for local models of some Shimura varieties
• Integral models of Shimura varieties with parahoric level structure
• Kottwitz's nearby cycles conjecture for a class of unitary Shimura\n varieties
• Nearby cycles on the local model for the GU(n-1,1) PEL Shimura variety over a ramified prime
• Local models of Shimura varieties and a conjecture of Kottwitz