On depth in the local Langlands correspondence for tori

TL;DR

This paper investigates the behavior of depth in the local Langlands correspondence for tori over non-archimedean local fields, providing an asymptotic analysis of how depth varies.

Contribution

It establishes an asymptotic result for the depths in the local Langlands correspondence specifically for tori over non-archimedean local fields.

Findings

Depth exhibits specific asymptotic behavior in the correspondence.

Provides new insights into the structure of the correspondence for tori.

Enhances understanding of depth-related properties in local Langlands theory.

Abstract

Let $K$ be a non-archimedean local field. In the local Langlands correspondence for tori over $K$, we prove an asymptotic result for the depths.