# Bounds on the number of simple modules in blocks of finite groups of Lie type

## TL;DR

This paper establishes upper bounds on the number of simple modules in certain blocks of finite groups of Lie type, specifically for quasi-isolated $ ext{l}$-blocks of exceptional groups over finite fields, when $ ext{l}$ is a bad prime.

## Contribution

It provides new upper bounds for the number of simple modules in quasi-isolated blocks of finite groups of Lie type of exceptional type, addressing cases where the prime is bad.

## Key findings

- Upper bounds on simple modules in quasi-isolated blocks
- Results for groups of exceptional Lie type over finite fields
- Addresses cases with bad primes for the group

## Abstract

Let $G$ be a simple, simply connected linear algebraic group of exceptional type defined over $\mathbb{F}_q$ with Frobenius endomorphism $F: G \to G$. In this work we give upper bounds on the number of simple modules in the quasi-isolated $\ell$-blocks of $G^F$ and $G^F/Z(G^F)$ when $\ell$ is bad for $G$.