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

Equivariant line bundles with connection on the p-adic upper half plane