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Prismatic crystals and $q$-Higgs fields
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abstract
Similarly to the theory of crystalline cohomology, we give a local description of a prismatic crystal and its cohomology in terms of a $q$-Higgs module and the associated $q$-Higgs complex on the bounded prismatic envelope of an embedding into a framed smooth algebra, when the base bounded prism is defined over the $q$-crystalline prism. We also discuss its behavior under the scalar extension by the Frobenius lifting and tensor products, and a global description of the cohomology of a prismatic crystal via Zariski cohomological descent.
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Cited by 1 Pith paper
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Prismatic cohomology and $A_{\inf}$-cohomology with coefficients
Prismatic cohomology of a locally finite free prismatic crystal is canonically isomorphic to A_inf-cohomology of the associated relative Breuil-Kisin-Fargues module, for smooth p-adic formal schemes over the ring of i...
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