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September 5, 2025Open Access

Hodge stratification in low ramification

Key Points

Hodge stratification demonstrates significant effects for shimura varieties with a ramification index less than or equal to 2.
The study introduces several polygons related to the ramification index of 3, enhancing understanding of the structure involved.
Understanding these stratifications provides insights into the sheaf of differentials associated with these mathematical structures.
The analysis shows that low ramification indices lead to a strong stratification, impacting classification and structural properties.

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≤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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Cite This Study

Stéphane Bijakowski (Thu,) studied this question.

synapsesocial.com/papers/68bb3ef02b87ece8dc9576a5 https://doi.org/https://doi.org/10.5802/pmb.59

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