After introducing the semistable comparison theorem for proper varieties with semistable reduction, I will discuss Beilinson’s generalization, in which he defined Hyodo-Kato cohomology for algebraic varieties and established the semistable comparison theorem without assuming properness, smoothness, or the existence of good models. I will then explain the construction of Hyodo-Kato cohomology for rigid analytic varieties, which was recently developed by Colmez-Niziol. Finally, I will outline some properties of Hyodo-Kato cohomology in the context of rigid analytic geometry.
