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Main Author: Micolet, Gabriel
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2505.12488
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author Micolet, Gabriel
author_facet Micolet, Gabriel
contents Let $F$ be a totally real field, $p$ a prime that we allow to ramify in $F$, and $B$ a quaternion algebra over $F$ which is split at places over $p$. We consider a smooth $p$-adic integral model, the Pappas-Rapoport model, of the Quaternionic Shimura variety attached to $B$ with prime-to-$p$ level, and the Goren-Oort stratification of its characteristic $p$ fiber. Furthermore, we also introduce Pappas-Rapoport models at Iwahori level $p$ along with a stratification of their characteristic $p$ fiber. We prove that these strata are isomorphic to products of $\mathbb{P}^1$-bundles over auxiliary Quaternionic Shimura varieties, from which we deduce the corresponding description of the Goren-Oort strata.
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spellingShingle A mod $p$ Geometric Jacquet-Langlands Relation for Quaternionic Shimura Varieties at Ramified Primes
Micolet, Gabriel
Number Theory
Let $F$ be a totally real field, $p$ a prime that we allow to ramify in $F$, and $B$ a quaternion algebra over $F$ which is split at places over $p$. We consider a smooth $p$-adic integral model, the Pappas-Rapoport model, of the Quaternionic Shimura variety attached to $B$ with prime-to-$p$ level, and the Goren-Oort stratification of its characteristic $p$ fiber. Furthermore, we also introduce Pappas-Rapoport models at Iwahori level $p$ along with a stratification of their characteristic $p$ fiber. We prove that these strata are isomorphic to products of $\mathbb{P}^1$-bundles over auxiliary Quaternionic Shimura varieties, from which we deduce the corresponding description of the Goren-Oort strata.
title A mod $p$ Geometric Jacquet-Langlands Relation for Quaternionic Shimura Varieties at Ramified Primes
topic Number Theory
url https://arxiv.org/abs/2505.12488