# A note on fierce ramification

## TL;DR

This paper demonstrates that bounding ramification at infinity implies fierce ramification, providing a positive answer to a question posed by Deligne regarding ramification behavior.

## Contribution

It establishes a link between bounded ramification at infinity and fierce ramification, resolving a question in ramification theory.

## Key findings

- Bounding ramification at infinity implies fierce ramification.
- Provides a positive answer to Deligne's question.
- Advances understanding of ramification behavior at infinity.

## Abstract

We show that bounding ramification at infinity bounds fierce ramification. This answers positively a question of Deligne posed to the first named author.