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arxiv 2308.09423 v1 pith:AIFXJ75K submitted 2023-08-18 math.AG math.NT

Overconvergent prismatic cohomology

classification math.AG math.NT
keywords cohomologyoverconvergentprismaticsmoothversionadicbesidesbhatt
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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 \'{e}tale cohomology of its generic fibre. Besides, I give an overconvergent version of the complex $A\Omega$ of Bhatt-Morrow-Scholze and relate it to overconvergent prismatic cohomology.

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