Good reductions of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic. Part I

Abstract

We prove the existence of good smooth integral models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic $(0,p)$. As a first application we provide a smooth solution (answer) to a conjecture (question) of Langlands for Shimura varieties of Hodge type. As a second application we prove the existence in arbitrary unramified mixed characteristic $(0,p)$ of integral canonical models of projective Shimura varieties of Hodge type with respect to h--hyperspecial subgroups as pro-étale covers of Néron models; this forms progress towards the proof of conjectures of Milne and Reimann. Though the second application was known before in some cases, its proof is new and more of a principle.

87 pages. Final version, to appear in Mathematische Nachrichten (most alignment issues kept loose to match with the layout of the journal)

References in corpus (4)

• On two theorems for flat, affine group schemes over a discrete valuation ring
• Level m stratifications of versal deformations of p-divisible groups
• A purity theorem for abelian schemes
• Integral models in unramified mixed characteristic (0,2) of hermitian orthogonal Shimura varieties of PEL type, Part II

Cited by in corpus (5)

• Rapoport-Zink spaces of Hodge type
• Ekedahl-Oort strata for good reductions of Shimura varieties of Hodge type
• Geometry of Shimura varieties of Hodge type over finite fields
• Geometric Satake, categorical traces, and arithmetic of Shimura varieties
• Perfectoid Shimura varieties of abelian type