Twists of Drinfeld–Stuhler Modular Varieties

Abstract

Let $\mathcal{A}$ be a maximal (or more generally a hereditary) order in a central simple algebra over a global field $F$ of positive characteristic. We show that certain modular scheme of $\mathcal{A}$-elliptic sheaves – for different $\mathcal{A}$ – are twists of each other and deduce that the *uniformization at *$\infty$ and the Cherednik-Drinfeld uniformization for these varieties are equivalent.