Hyodo-Kato cohomology in rigid geometry: some foundational results
Xinyu Shao
TL;DR
This paper develops foundational results for Hyodo-Kato cohomology in rigid geometry, proving the semistable conjecture for étale cohomology of almost proper varieties and establishing GAGA comparison results.
Contribution
It introduces the Gysin sequence for Hyodo-Kato cohomology and proves key conjectures, advancing the understanding of cohomological properties in rigid analytic geometry.
Findings
Proved the semistable conjecture for étale cohomology.
Established GAGA comparison for Hyodo-Kato cohomology.
Constructed the Gysin sequence using open-closed sequences and Poincaré duality.
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology