This analysis reveals the impact of hodge stratification on shimura varieties, suggesting strong effects under low ramification indices.
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≤3). For e≤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.
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Stéphane Bijakowski (2025) studied this question.
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