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Integral models in unramified mixed characteristic \((0,2)\) of Hermitian orthogonal Shimura varieties of PEL type. II. (English) Zbl 1305.11056
The paper under review is a continuation of an earlier work [J. Ramanujan Math. Soc. 27, No. 4, 425–477 (2012; Zbl 1357.11062)] of the author. Its main goal is to prove the existence of integral canonical models of the so-called hermitian orthogonal Shimura varieties of PEL type in unramified mixed characteristic \((0,2)\). These PEL Shimura varieties are moduli spaces of polarized abelian schemes equipped with a suitable endomorphism algebra and level structure. The method in the paper is somehow standard – to prove the regularity and formal smoothness of the normalization of the schematic closure of a natural subscheme; however the technique is of high level.
Reviewer: Xin Lu (Mainz)

MSC:
11G18 Arithmetic aspects of modular and Shimura varieties
14G35 Modular and Shimura varieties
11G10 Abelian varieties of dimension \(> 1\)
11G15 Complex multiplication and moduli of abelian varieties
14F30 \(p\)-adic cohomology, crystalline cohomology
14K10 Algebraic moduli of abelian varieties, classification
14L05 Formal groups, \(p\)-divisible groups
11E57 Classical groups
20G25 Linear algebraic groups over local fields and their integers
Citations:
Zbl 1357.11062
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