A mod p geometric Jacquet-Langlands relation for Hilbert modular varieties at ramified primes

by Gabriel Micolet

Thursday May 15, 2025, 2:00 PM → 4:00 PM Europe/Paris

M7 411 (ENS Lyon)

Let F be a totally real field and p a prime which we allow to ramify in F. In this talk, I will discuss an integral p-adic model, the Pappas-Rapoport splitting model, of the Hilbert modular variety at some tame level. This model is smooth of relative dimension d=[F:Q] and agrees with the usual model if p is unramified. I will show that the closed strata of the Goren-Oort stratification of its special fiber are isomorphic to a product of P^1 bundles over (splitting models of) auxiliary quaternionic Shimura varieties. In fact, I will show how this follows from a similar description of the closed strata of the special fiber of Pappas-Rapoport models with Iwahori level at primes over p. This extends the work of Tian-Xiao and Diamond-Kassaei-Sasaki. Time permitting, I will discuss some applications to the study of mod p Hilbert modular forms and how these results apply to more general quaternionic Shimura varieties.