Geodesic
Mod p points on shimura varieties of parahoric level
Forum of Mathematics, Pi, Tome 12 (2024)

Voir la notice de l'article provenant de la source Cambridge University Press

We study the $\overline {\mathbb {F}}_{p}$-points of the Kisin–Pappas integral models of Shimura varieties of Hodge type with parahoric level. We show that if the group is quasi-split, then every isogeny class contains the reduction of a CM point, proving a conjecture of Kisin–Madapusi–Shin. We, furthermore, show that the mod p isogeny classes are of the form predicted by the Langlands–Rapoport conjecture (cf. Conjecture 9.2 of [Rap05]) if either the Shimura variety is proper or if the group at p is unramified. The main ingredient in our work is a global argument that allows us to reduce the conjecture to the case of very special parahoric level. This case is dealt with in the Appendix by Zhou. As a corollary to our arguments, we determine the connected components of Ekedahl–Oort strata. 
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Pol van Hoften. Mod p points on shimura varieties of parahoric level. Forum of Mathematics, Pi, Tome 12 (2024). doi: 10.1017/fmp.2024.22

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