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

Lambert A'Campo; Bence Hevesi; Jack A. Thorne; Dmitri Whitmore

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

Number Theory 2026-07-13 v1

Authors: Lambert A'Campo , Bence Hevesi , Jack A. Thorne , Dmitri Whitmore

Abstract

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.

Keywords

local-global compatibility automorphic Galois representations CM fields p-adic Hodge theory local Langlands correspondence

Cite

@article{arxiv.2607.11763,
  title  = {Local-global compatibility of automorphic Galois representations over CM fields at $p$},
  author = {Lambert A'Campo and Bence Hevesi and Jack A. Thorne and Dmitri Whitmore},
  journal= {arXiv preprint arXiv:2607.11763},
  year   = {2026}
}