On the structure of some p-adic period domains

Miaofen Chen School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, China Laurent Fargues CNRS, Institut de Mathématiques de Jussieu, Paris, France Xu Shen Morningside Center of Mathematics, Academy of Mathematics and Systems Science, C.A.S., Beijing, China

Number Theory Algebraic Geometry mathscidoc:2203.24003

Cambridge Journal of Mathematics, 9, (1), 213-267, 2021.10
We study the geometry of the p‑adic analogues of the complex analytic period spaces first introduced by Griffiths. More precisely, we prove the Fargues–Rapoport conjecture for p‑adic period domains: for a reductive group G over a p‑adic field and a minuscule cocharacter μ of G, the weakly admissible locus coincides with the admissible one if and only if the Kottwitz set B(G,μ) is fully Hodge–Newton decomposable.
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  title={On the structure of some p-adic period domains},
  author={Miaofen Chen, Laurent Fargues, and Xu Shen},
  booktitle={Cambridge Journal of Mathematics},
Miaofen Chen, Laurent Fargues, and Xu Shen. On the structure of some p-adic period domains. 2021. Vol. 9. In Cambridge Journal of Mathematics. pp.213-267. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220317151627371916990.
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