arXiv subjects

Bence Hevesi

Publications and source records attributed to Bence Hevesi.

4 recordsLinked to original sources

arXiv2026

Local-global compatibility of automorphic Galois representations over CM fields at $p$

Let $F$ be a CM number field; then, to any cuspidal, regular algebraic automorphic representation of $\mathrm{GL}_n(\mathbf{A}_F)$ is associated a compatible system of $p$-adic Galois representations of the absolute Galois group of $F$. We prove that these representations are potentially semi-stable, in the sense of $p$-adic Hodge theory, and satisfy compatibility with the local Langlands correspondence, up to semi-simplification.

math.NT↗

arXiv2026

Adjoint Bloch--Kato Selmer groups of regular algebraic automorphic Galois representations

We prove the vanishing of the adjoint Bloch--Kato Selmer group of the Galois representations associated to regular algebraic automorphic representations of general linear groups over CM fields. A key novelty of our work is that we impose conditions only on the $p$-adic Galois representations, and not on their associated residual representations modulo $p$.

math.NT↗

arXiv2026

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

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.

math.NT↗

arXiv2024

Ordinary parts and local-global compatibility at $\ell=p$

We prove local-global compatibility results at $\ell=p$ for the torsion automorphic Galois representations constructed by Scholze, generalising the work of Caraiani--Newton. In particular, we verify, up to a nilpotent ideal, the local-global compatibility conjecture at $\ell=p$ of Gee--Newton in the case of imaginary CM fields under some technical assumptions. The key new ingredient is a local-global compatibility result for $Q$-ordinary self-dual automorphic representations for arbitrary parabolic subgroups.

math.NT↗