$\mathscr{D}$-elliptic sheaves and the Hasse principle
$\mathscr{D}$-elliptic sheaves and the Hasse principle
Let $p$ be a rational prime, $q>1$ a power of $p$ and $F=\mathbb{F}_q(t)$. For an integer $d\geq 2$, let $D$ be a central division algebra over $F$ of dimension $d^2$ which is split at $\infty$ and has invariant $\mathrm{inv}_x(D)=1/d$ at any place $x$ of $F$ at which $D$ ramifies. Let …