Hodge stratification in low dimension

Abstract

We define and study the Hodge stratification for the special fiber of Shimura varieties defined with the Pappas-Rapoport condition, in the case of low ramification index ($e\le 3$). For $e\le 2$, the Hodge polygon induces a strong stratification. For $e=3$, one needs to introduce several polygons. They describe the isomorphism class of the sheaf of differentials with extra structure, and induce a strong stratification on the variety.