The product structure of Newton strata in the good reduction of Shimura varieties of Hodge type

We construct a generalisation of Mantovan’s almost product structure to Shimura varieties of Hodge type with hyperspecial level structure at p p and deduce that the perfection of the Newton strata are proétale 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 and Scholze’s generalisation of the almost product structure for Shimura varieties of Hodge type.