Hyodo-Kato cohomology in rigid geometry: some foundational results

Abstract: By exploring the geometric properties of Hyodo-Kato cohomology in rigid geometry, we establish several foundational results, including the semistable conjecture for \'etale cohomology of almost proper rigid analytic varieties, and GAGA (comparison between algebraic and analytic) for Hyodo-Kato cohomology. A central component of our approach is the Gysin sequence for Hyodo-Kato cohomology, which we construct using the open-closed exact sequence for compactly supported Hyodo-Kato cohomology and Poincar\'e duality.