On Goren-Oort stratification for quaternionic Shimura varieties

Abstract

Let $F$ be a totally real field in which $p$ is unramified. We study the Goren-Oort stratification of the special fibers of quaternionic Shimura varieties over a place above $p$. We show that each stratum is a $({\mathbb{P}}^1{)}^N$-bundle over other quaternionic Shimura varieties (for some appropriate $N$).

78 pages. This version will appear in Comp. Math

References in corpus (2)

• Hilbert modular forms and p-adic Hodge theory
• Towards a Jacquet-Langlands correspondence for unitary Shimura varieties

Cited by in corpus (8)

• On Tate conjecture for the special fibers of some unitary Shimura varieties
• Minimal weights of Hilbert modular forms in characteristic p
• The cone of minimal weights for mod $p$ Hilbert modular forms
• Supersingular locus of Hilbert modular varieties, arithmetic level raising and Selmer groups
• Tate cycles on some quaternionic Shimura varieties mod p
• An intriguing hyperelliptic Shimura curve quotient of genus 16
• Plectic structures in p-adic de Rham cohomology
• On the cohomology of some simple Shimura varieties with bad reduction