摘要翻译：
证明了Hodge型Shimura变种在任意未分支混合特征$(0,p)$下的良好光滑积分模型的存在性。作为第一个应用，我们给出了Hodge型Shimura变种的Langlands猜想（问题）的光滑解（答案）。作为第二个应用，我们证明了关于H-超特殊子群的Hodge型射影Shimura簇的积分规范模型在任意未分支混合特征$(0，p)$中的存在性，作为N-eron模型的Pro-etale覆盖；这形成了对米尔恩和雷曼猜想的证明的进展。虽然第二个应用程序以前在某些情况下是众所周知的，但它的证明是新的，更像是一个原则。
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英文标题：
《Good reductions of Shimura varieties of Hodge type in arbitrary
  unramified mixed characteristic. Part I》
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作者：
Adrian Vasiu
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最新提交年份：
2020
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分类信息：

一级分类：Mathematics        数学
二级分类：Number Theory        数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  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-\'etale covers of N\'eron 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.
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PDF链接：
https://arxiv.org/pdf/0707.1668