On the non-generic part of cohomology of compact unitary Shimura varieties of signature $(1,n)$

Kun Liu

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arXiv · 2511.18629

On the non-generic part of cohomology of compact unitary Shimura varieties of signature $(1,n)$

Kun Liu

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Abstract

In this short note, we prove a result about the non-generic part of the cohomology of certain compact unitary Shimura varieties for good $p$, partially extending a result of Boyer in the case of Harris--Taylor unitary Shimura varieties. Our arguments are different to those of Boyer -- we work in the context of the work of Fargues--Scholze, using ideas introduced by Koshikawa to study the generic part of cohomology.

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Kun Liu. 2025-11-23. On the non-generic part of cohomology of compact unitary Shimura varieties of signature $(1,n)$. https://arxiv.org/abs/2511.18629

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