Comparison of prismatic cohomology and derived de Rham cohomology

  • Shizhang Li

    Chinese Academy of Sciences, Beijing, China
  • Tong Liu

    Purdue University, West Lafayette, USA
Comparison of prismatic cohomology and derived de Rham cohomology cover

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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 is a proper smooth formal scheme over with being a -adic field, we improve Breuil–Caruso’s theory on comparison between torsion crystalline cohomology and torsion étale cohomology.

Cite this article

Shizhang Li, Tong Liu, Comparison of prismatic cohomology and derived de Rham cohomology. J. Eur. Math. Soc. (2023), published online first

DOI 10.4171/JEMS/1377