2023/08/18 by Andreas Langer, Langer, Andreas
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2308.09423
openalex publication_date 2023/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note I define an overconvergent version of prisms and prismatic cohomology as introduced by Bhatt and Scholze and show that overconvergent prismatic cohomology specialises to p-adic cohomologies, like Monsky-Washnitzer resp. rigid cohomology for smooth varieties over a perfect field, the de Rham cohomology of smooth weak formal schemes over a perfectoid ring and the étale cohomology of its generic fibre. Besides, I give an overconvergent version of the complex AΩ of Bhatt-Morrow-Scholze and relate it to overconvergent prismatic cohomology.