Local-global compatibility at $p\neq\ell$ for torsion automorphic forms

Bence Hevesi

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arXiv · 2606.31698

Local-global compatibility at $p\neq\ell$ for torsion automorphic forms

Bence Hevesi

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Abstract

We prove local-global compatibility results at $p \neq \ell$ for the automorphic group determinants constructed by Scholze, generalising the result of Varma to torsion classes appearing in Betti cohomology. Our argument combines the construction of Scholze with the theory of representations of $p$-adic general linear groups with $\mathbf{Z}_{\ell}$-coefficients.

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Bence Hevesi. 2026-06-30. Local-global compatibility at $p\neq\ell$ for torsion automorphic forms. https://arxiv.org/abs/2606.31698

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