An alternative construction of zip period maps for Shimura varieties

Let \(S\) be the special fibre of a Shimura variety of Hodge type, with good reduction at a place above \(p\). We give an alternative construction of the zip period map for \(S\), which is used to define the Ekedahl-Oort strata of \(S\). The method employed is local, \(p\)-adic, and group-theoretic in nature.