# Normal distribution of bad reduction

## TL;DR

This paper shows that primes of bad reduction in families of curves follow a normal distribution when ordered by height.

## Contribution

The novelty is proving normal distribution laws for primes of bad semistable reduction in such families.

## Key findings

- Primes of bad semistable reduction follow a normal distribution in families of curves.
- Almost all curves in these families have many primes of bad reduction when ordered by height.

## Abstract

We prove normal distribution laws for primes of bad semistable reduction in families of curves. As a consequence, we deduce that when ordered by height, \documentclass[12pt]{minimal}
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\begin{document}$$100\%$$\end{document}100% of curves in these families have, in a precise sense, many such primes.