$p$-Adic Hodge Theory for Artin Stacks

Dmitry Kubrak, Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France. Artem Prikhodko, National Research University, Moscow, Russia, and Center for Advanced Studies, Moscow, Russia.

Chapters 1. Introduction 2. Hodge-proper stacks 3. De Rham, crystalline, and prismatic cohomology of stacks 4. Etale sheaves on geometric stacks 5. Etale cohomology of stacks 6. Local acyclicity of some quotient stacks 7. Applications A. Geometric stacks and quasi-coherent sheaves B. Fontaine's infinitesimal period ring ${A_{\mathrm {inf}}}$ C. Totalizations and coconnectivity