# The Brauer group of $\mathscr{M}_{1,1}$ over algebraically closed fields of characteristic $2$

## TL;DR

This paper determines the Brauer group of the moduli stack of elliptic curves over algebraically closed fields of characteristic 2, showing it is isomorphic to Z/2, and extends the computation to finite fields.

## Contribution

It provides the first explicit computation of the Brauer group of ,1 moduli stack in characteristic 2, revealing its structure as Z/2 over algebraically closed fields.

## Key findings

- Brauer group over algebraically closed fields is Z/2
- Brauer group over finite fields of characteristic 2 computed
- Extends understanding of moduli stacks in characteristic 2

## Abstract

We prove that the Brauer group of the moduli stack of elliptic curves $\mathscr{M}_{1,1,k}$ over an algebraically closed field $k$ of characteristic $2$ is isomorphic to $\mathbb{Z}/(2)$. We also compute the Brauer group of $\mathscr{M}_{1,1,k}$ where $k$ is a finite field of characteristic $2$.