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Normalization in integral models of Shimura varieties of Hodge type

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 Added by Yujie Xu
 Publication date 2020
  fields
and research's language is English
 Authors Yujie Xu




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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 integral model $mathscr{S}_{K}(mathrm{GSp},S^{pm})$ for a Siegel modular variety. In particular, the normalization step in the construction of $mathscr{S}_K(G,X)$ is redundant. In particular, our results apply to the earlier integral models constructed by Rapoport and Kottwitz, as those models agree with the Hodge type integral models for appropriately chosen Shimura data.



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