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Mathematische Zeitschrift

, Volume 291, Issue 1–2, pp 329–363 | Cite as

On central leaves of Hodge-type Shimura varieties with parahoric level structure

  • Wansu KimEmail author
Article
  • 93 Downloads

Abstract

Kisin and Pappas (Publ Math Inst Hautes Études Sci, 2018) constructed integral models of Hodge-type Shimura varieties with parahoric level structure at \(p>2\), such that the formal neighbourhood of a mod p point can be interpreted as a deformation space of p-divisible group with some Tate cycles (generalising Faltings’ construction). In this paper, we study the central leaf and the closed Newton stratum in the formal neighbourhoods of mod p points of Kisin–Pappas integral models with parahoric level structure; namely, we obtain the dimension of central leaves and the almost product structure of Newton strata. In the case of hyperspecial level structure (i.e., in the good reduction case), our main results were already obtained by Hamacher (Math Z 287(3–4):1255–1277, 2017), and we show that the result of this paper holds for ramified groups as well.

Keywords

Shimura varieties of Hodge type Deformations of p-divisible groups 

Mathematics Subject Classification

14L05 14G35 

Notes

Acknowledgements

The author thanks Paul Hamacher for many helpful discussions, and Julien Hauseux for his help with group theory used in the proof of Proposition 3.1.4. The author would also like to thank the anonymous referee whose comments were greatly helpful. This work was supported by the EPSRC (Engineering and Physical Sciences Research Council) in the form of EP/L025302/1.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.KIAS, Department of MathematicsSeoulSouth Korea

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