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Fully HodgeNewton decomposable Shimura varieties

Ulrich Goertz Xuhua He Sian Nie

Algebraic Geometry mathscidoc:1912.43203

Peking Mathematical Journal, 2, (2), 99-154, 2019.6
The motivation for this paper is the study of arithmetic properties of Shimura varieties, in particular the Newton stratification of the special fiber of a suitable integral model at a prime with parahoric level structure. This is closely related to the structure of RapoportZink spaces and of affine DeligneLusztig varieties. We prove a HodgeNewton decomposition for affine DeligneLusztig varieties and for the special fibers of RapoportZink spaces, relating these spaces to analogous ones defined in terms of Levi subgroups, under a certain condition (HodgeNewton decomposability) which can be phrased in combinatorial terms. Second, we study the Shimura varieties in which every non-basic\sigma-isogeny class is HodgeNewton decomposable. We show that (assuming the axioms of He and Rapoport in Manuscr. Math. 152 (34): 317343, 2017) this condition is equivalent to nice conditions on either the basic locus or on
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@inproceedings{ulrich2019fully,
  title={Fully HodgeNewton decomposable Shimura varieties},
  author={Ulrich Goertz, Xuhua He, and Sian Nie},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112923127899763},
  booktitle={Peking Mathematical Journal},
  volume={2},
  number={2},
  pages={99-154},
  year={2019},
}
Ulrich Goertz, Xuhua He, and Sian Nie. Fully HodgeNewton decomposable Shimura varieties. 2019. Vol. 2. In Peking Mathematical Journal. pp.99-154. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112923127899763.
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