English

Tame categorical local Langlands correspondence

Representation Theory 2025-04-11 v1 Algebraic Geometry

Abstract

In one of our previous articles, we outlined the formulation of a version of the categorical arithmetic local Langlands conjecture. The aims of this article are threefold. First, we provide a detailed account of one component of this conjecture: the local Langlands category. Second, we aim to prove this conjecture in the tame case for quasi-split unramified reductive groups. Finally, we will explore the first applications of such categorical equivalence.

Keywords

Cite

@article{arxiv.2504.07482,
  title  = {Tame categorical local Langlands correspondence},
  author = {Xinwen Zhu},
  journal= {arXiv preprint arXiv:2504.07482},
  year   = {2025}
}

Comments

Preliminary version. We anticipate another round of editing, with some new results to be added before submission. The current version will serve as a reference for several other articles. Feedback is welcome!