On the Newton stratification in the good reduction of Shimura varieties

TL;DR

This paper generalizes Mantovan's almost product structure to Shimura varieties of Hodge type, showing that their Newton strata's perfections are locally isomorphic to products of central leaves and Rapoport-Zink spaces, extending existing results.

Contribution

It extends the almost product structure to a broader class of Shimura varieties and establishes local isomorphisms for their Newton strata's perfections.

Findings

Perfections of Newton strata are pro-étale locally isomorphic to products of central leaves and Rapoport-Zink spaces.

The almost product formula is extended to Shimura varieties of Hodge type.

Provides a framework for understanding the structure of Newton strata in these varieties.

Abstract

I construct a generalisation of Mantovan's almost product structure to Shimura varieties of Hodge type with hyperspecial level structure at $p$ and deduce that the perfection of the Newton strata are pro-\'etale locally isomorphic to the perfection of the product of a central leaf and a Rapoport-Zink space. The almost product formula can be extended to obtain an analogue of Caraiani's and Scholze's generalisation of the almost product structure for Shimura varieties of Hodge type.