Tame categorical local Langlands correspondence

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.

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!