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

Bence Hevesi

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

Number Theory 2026-06-30 v1 Representation Theory

Authors: Bence Hevesi

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.

Keywords

local-global compatibility torsion automorphic forms Galois representations Betti cohomology p-adic general linear groups

Cite

@article{arxiv.2606.31698,
  title  = {Local-global compatibility at $p\neq\ell$ for torsion automorphic forms},
  author = {Bence Hevesi},
  journal= {arXiv preprint arXiv:2606.31698},
  year   = {2026}
}