Remarks on Ekedahl-Oort stratifications
  This short paper is a continuation of the author's Ph.D thesis, where Ekedahl-Oort strata are defined and studied for Shimura varieties of Hodge type. The main results here are as follows.   1. The Ekedahl-Oort stratification is independent of the choices of symplectic embeddings.   2. Under certain reasonable assumptions, there is certain functoriality for Ekedahl-Oort stratifications with respect to morphisms of Shimura varieties. 
Chao Zhang
math.AG