Logarithmic de Rham comparison for open rigid spaces

Abstract

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

Add references. 39 pages, comments welcome v2: final version, 40 pages, comments still welcome

References in corpus (3)

• Logarithmic Riemann-Hilbert correspondences for rigid varieties
• Foundations of Logarithmic Adic Spaces
• Artin vanishing in rigid analytic geometry

Cited by in corpus (2)

• Hyodo-Kato theory with syntomic coefficients
• On uniqueness of $p$-adic period morphisms, II