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

TL;DR

This paper investigates the non-generic cohomology of specific compact unitary Shimura varieties at good primes, extending previous results with new methods based on Fargues-Scholze and Koshikawa's ideas.

Contribution

It provides a novel proof about the non-generic cohomology of certain Shimura varieties, differing from Boyer's approach and leveraging recent advances in the field.

Findings

Proves a new result on non-generic cohomology of compact unitary Shimura varieties.

Extends Boyer's results to a broader class of Shimura varieties.

Introduces a different proof technique using Fargues-Scholze and Koshikawa's ideas.

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.