Abstract
We establish a comparison isomorphism between prismatic cohomology and derived de Rham cohomology respecting various structures, such as their Frobenius actions and filtrations. As an application, when X is a proper smooth formal scheme over \mathcal{O}_K with K being a p -adic field, we improve Breuil–Caruso’s theory on comparison between torsion crystalline cohomology and torsion étale cohomology.
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