Geodesic
On Some Generalized Rapoport–Zink Spaces
Canadian journal of mathematics, Tome 72 (2020) no. 5, pp. 1111-1187

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

We enlarge the class of Rapoport–Zink spaces of Hodge type by modifying the centers of the associated $p$-adic reductive groups. Such obtained Rapoport–Zink spaces are said to be of abelian type. The class of Rapoport–Zink spaces of abelian type is strictly larger than the class of Rapoport–Zink spaces of Hodge type, but the two type spaces are closely related as having isomorphic connected components. The rigid analytic generic fibers of Rapoport–Zink spaces of abelian type can be viewed as moduli spaces of local $G$-shtukas in mixed characteristic in the sense of Scholze.We prove that Shimura varieties of abelian type can be uniformized by the associated Rapoport–Zink spaces of abelian type. We construct and study the Ekedahl–Oort stratifications for the special fibers of Rapoport–Zink spaces of abelian type. As an application, we deduce a Rapoport–Zink type uniformization for the supersingular locus of the moduli space of polarized K3 surfaces in mixed characteristic. Moreover, we show that the Artin invariants of supersingular K3 surfaces are related to some purely local invariants.
DOI : 10.4153/S0008414X19000269
Mots-clés : Rapoport–Zink space, shtuka, Shimura variety, K3 surface 
Shen, Xu. On Some Generalized Rapoport–Zink Spaces. Canadian journal of mathematics, Tome 72 (2020) no. 5, pp. 1111-1187. doi: 10.4153/S0008414X19000269
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