  Recently, Darmon and Vonk initiated the theory of rigid meromorphic cocycles
for the group $\mathrm{SL}_2(\mathbb{Z}[1/p])$. One of their major results is
the algebraicity of the divisor associated to such a cocycle. We generalize the
result to the setting of $\mathfrak{p}$-arithmetic subgroups of inner forms of
$\mathrm{SL}_2$ over arbitrary number fields. The method of proof differs from
the one of Darmon and Vonk. Their proof relies on an explicit description of
the cohomology via modular symbols and continued fractions, whereas our main
tool is Bieri-Eckmann duality for arithmetic groups.
