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In this note, we prove the logarithmic $p$-adic comparison theorem for openrigid analytic varieties. We prove that a smooth rigid analytic variety with astrict simple normal crossing divisor is locally $K(\pi,1)$ (in a certainsense) with respect to $\mathbb{F}_p$-local systems and ramified coveringsalong the divisor. We follow Scholze's method to produce a pro-version of theFaltings site and use this site to prove a primitive comparison theorem in oursetting. After introducing period sheaves in our setting, we prove aforesaidcomparison theorem.

Logarithmic de Rham comparison for open rigid spaces