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

Abstract

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

arXiv comment33 pages; corrected some mistakes; added the finite field case