HODGE STRATIFICATION IN LOW RAMIFICATION

Stéphane Bijakowski

doi:10.5802/pmb.59

HODGE STRATIFICATION IN LOW RAMIFICATION

Stéphane Bijakowski

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	5-20
Number of pages	16
Journal	Publications Mathematiques de Besancon - Algebre et Theorie des Nombres
Volume	2025
DOIs	https://doi.org/10.5802/pmb.59
Publication status	Published - 1 Jan 2025

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AB - 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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HODGE STRATIFICATION IN LOW RAMIFICATION

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