# A note on depth preservation

## TL;DR

This paper demonstrates that for certain wildly ramified tori, the depth characteristic is not maintained under the local Langlands correspondence, highlighting a specific limitation in the current understanding.

## Contribution

It reveals that depth preservation fails for wildly ramified tori in the local Langlands correspondence, providing new insights into ramification behavior.

## Key findings

- Depth is not preserved for wildly ramified tori.
- The failure of depth preservation is specific to certain ramification conditions.
- This challenges assumptions about the general behavior of the local Langlands correspondence.

## Abstract

We show that for a wildly ramified torus, depth is not preserved in general under local Langlands correspondence for tori.