ﻻ يوجد ملخص باللغة العربية
A p-divisible group, or more generally an F-crystal, is said to be Hodge-Newton reducible if its Hodge polygon passes through a break point of its Newton polygon. Katz proved that Hodge-Newton reducible F-crystals admit a canonical filtration called the Hodge-Newton filtration. The notion of Hodge-Newton reducibility plays an important role in the deformation theory of p-divisible groups; the key property is that the Hodge-Newton filtration of a p-divisible group over a field of characteristic p can be uniquely lifted to a filtration of its deformation. We generalize Katzs result to F-crystals that arise from an unramified local Shimura datum of Hodge type. As an application, we give a generalization of Serre-Tate deformation theory for local Shimura data of Hodge type. We also apply our deformation theory to study some congruence relations on Shimura varieties of Hodge type.
Let k be a perfect field of characteristic p>0. We prove the existence of ascending and descending slope filtrations for Shimura p-divisible objects over k. We use them to classify rationally these objects over bar k. Among geometric applications, we
The main purpose of this paper is to prove a group-theoretic generalization of a theorem of Katz on isocrystals. Along the way we reprove the group-theoretic generalization of Mazurs inequality for isocrystals due to Rapoport-Richartz, and generalize
In a previous paper, we constructed a category of (phi, Gamma)-modules associated to any adic space over Q_p with the property that the etale (phi, Gamma)-modules correspond to etale Q_p-local systems; these involve sheaves of period rings for Scholz
Let $(G,X)$ be a Shimura datum of Hodge type, and $mathscr{S}_K(G,X)$ its integral model with hyperspecial level structure. We prove that $mathscr{S}_K(G,X)$ admits a closed embedding, which is compatible with moduli interpretations, into the integra
We compute the Hodge numbers for the quotients of complete intersection Calabi-Yau three-folds by groups of orders divisible by 4. We make use of the polynomial deformation method and the counting of invariant Kahler classes. The quotients studied he