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arXiv · 2608.26721

Torsion-vanishing for Siegel modular varieties via supercuspidal congruences

Ana Caraiani·Sug Woo Shin
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Abstract

We prove that the generic part of the cohomology of Siegel modular varieties with torsion coefficients is concentrated above the middle degree, under a suitable notion of genericity that is optimal in the unramified case. Our method relies on the semi-perversity of the relative cohomology of the Igusa stack and on a trace formula computation that is made possible by a congruence technique introduced by Scholze and Fintzen--Shin. Compared with the work of Yang--Zhu, which handles Shimura varieties of abelian type via categorical local Langlands, our method is adapted to Siegel modular varieties but handles coefficients of arbitrarily small characteristic.

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Ana Caraiani, Sug Woo Shin. 2026-08-27. Torsion-vanishing for Siegel modular varieties via supercuspidal congruences. https://arxiv.org/abs/2608.26721

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