  Let $F$ be a finite extension of $\mathbb{Q}_p$, let $\Omega_F$ be Drinfeld's
upper half-plane over $F$ and let $G^0$ the subgroup of $GL_2(F)$ consisting of
elements whose determinant has norm $1$. By working locally on $\Omega_F$, we
construct and classify the torsion $G^0$-equivariant line bundles with
integrable connection on $\Omega$ in terms of the smooth linear characters of
the units of the maximal order of the quaternion algebra over $F$.
