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arXiv · 2505.04329

On the generic part of the cohomology of Shimura varieties of abelian type

Xiangqian Yang·Xinwen Zhu
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Abstract

This article contributes to the study of the generic part of the cohomology of Shimura varieties. Under a mild restriction of the characteristic of the coefficient field, we prove a torsion vanishing result for Shimura varieties of abelian type, confirming a conjecture by Hamann--Lee. Our proofs utilize the unipotent categorical local Langlands correspondence and, in contrast to previous works, do not rely on the endoscopic classification of representations or on other results established through trace formula techniques.

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Xiangqian Yang, Xinwen Zhu. 2025-05-07. On the generic part of the cohomology of Shimura varieties of abelian type. https://arxiv.org/abs/2505.04329

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