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Kisin and Pappas constructed integral models of Hodge-type Shimura varietieswith parahoric level structure at $p>2$, such that the formal neighbourhood ofa mod~$p$ point can be interpreted as a deformation space of $p$-divisiblegroup with some Tate cycles (generalising Faltings' construction). In thispaper, we study the central leaf and the closed Newton stratum in the formalneighbourhoods of mod~$p$ points of Kisin-Pappas integral models with parahoriclevel structure; namely, we obtain the dimension of central leaves and thealmost product structure of Newton strata. In the case of hyperspecial levelstrucure (i.e., in the good reduction case), our main results were alreadyobtained by Hamacher, and the result of this paper holds for ramified groups aswell.

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