Comparison of prismatic cohomology and derived de Rham cohomology
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 \'etale cohomology.
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Algebraic Geometry
Number Theory
14F30, 11F80
