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 integers of a perfectoid field.
Faltings,Ap-adic Simpson correspondence, Adv
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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 integers of a perfectoid field.