Franco-Asian Summer School on Arithmetic Geometry

Collection Franco-Asian Summer School on Arithmetic Geometry

Organizer(s) Ahmed Abbes (CNRS & IHÉS), Ana Caraiani (Imperial College London ), Ariane Mézard (Sorbonne Université), Takeshi Saito (University of Tokyo), Takeshi Tsuji (The University of Tokyo), Daxin Xu (Chinese Academy of Sciences), Weizhe Zheng (Chinese Academy of Sciences).

Date(s) 30/05/2022 - 03/06/2022

linked URL https://www.ihes.fr/~abbes/Luminy/luminy2022.html

00:00:00 / 00:00:00

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Prismatic cohomology and A_inf-cohomology with coefficients

By Takeshi Tsuji

Similarly to crystalline cohomology theory, we give a local description of a prismatic crystal and its cohomology in terms of a q-Higgs module and its q-Dolbeault complex on a bounded prismatic envelope when the base prism is defined over the prism $Z_p[[q-1]]$. As an application, we obtain a comparison isomorphism between $A_{inf}$-cohomology of a relative Breuil-Kisin module, studied in a joint work with M. Morrow, and prismatic cohomology of the corresponding prismatic crystal. The result also can be applied to an analogous comparison in the integral p-adic Simpson correspondence.

Information about the video

Date of recording 30/05/2022
Date of publication 20/06/2022
Institution IHES
Language English
Audience Researchers, Graduate Students
Format MP4
Venue CIRM

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