Compactly supported $p$-adic pro-étale cohomology of analytic varieties

We study properties of compactly supported $p$-adic pro-étale cohomology of smooth partially proper rigid analytic varieties. In particular, we prove a comparison theorem, in a stable range, with compactly supported syntomic cohomology, which is built from compactly supported Hyodo-Kato and ${\mathcal{B}}_{\mathrm{d}\mathrm{r}}^{+}$-cohomologies. We derive from that a (limited version of a) fundamental diagram.