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

TL;DR

This paper investigates the structure of central leaves and Newton strata in the formal neighborhoods of mod p points of Hodge-type Shimura varieties with parahoric level structure, extending known results to ramified groups.

Contribution

It provides the dimension of central leaves and the almost product structure of Newton strata for parahoric level structures, generalizing previous results to ramified groups.

Findings

Determined the dimension of central leaves.

Established the almost product structure of Newton strata.

Extended results to ramified groups.

Abstract

Kisin and Pappas 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 strucure (i.e., in the good reduction case), our main results were already obtained by Hamacher, and the result of this paper holds for ramified groups as well.