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We construct a new cohomology theory for proper smooth (formal) schemes over the ring of integers of . It takes values in a mixed-characteristic analogue of Dieudonné modules, which was previously defined by Fargues as a version of Breuil–Kisin modules. Notably, this cohomology theory specializes to all other known -adic cohomology theories, such as crystalline, de Rham and étale cohomology, which allows us to prove strong integral comparison theorems.
The construction of the cohomology theory relies on Faltings’ almost purity theorem, along with a certain functor on the derived category, defined previously by Berthelot–Ogus. On affine pieces, our cohomology theory admits a relation to the theory of de Rham–Witt complexes of Langer–Zink, and can be computed as a -deformation of de Rham cohomology.
@article{PMIHES_2018__128__219_0,
author = {Bhatt, Bhargav and Morrow, Matthew and Scholze, Peter},
title = {Integral $p$-adic {Hodge} theory},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {219--397},
publisher = {Springer Berlin Heidelberg},
address = {Berlin/Heidelberg},
volume = {128},
year = {2018},
doi = {10.1007/s10240-019-00102-z},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-019-00102-z/}
}
TY - JOUR AU - Bhatt, Bhargav AU - Morrow, Matthew AU - Scholze, Peter TI - Integral $p$-adic Hodge theory JO - Publications Mathématiques de l'IHÉS PY - 2018 SP - 219 EP - 397 VL - 128 PB - Springer Berlin Heidelberg PP - Berlin/Heidelberg UR - http://geodesic.mathdoc.fr/articles/10.1007/s10240-019-00102-z/ DO - 10.1007/s10240-019-00102-z LA - en ID - PMIHES_2018__128__219_0 ER -
%0 Journal Article %A Bhatt, Bhargav %A Morrow, Matthew %A Scholze, Peter %T Integral $p$-adic Hodge theory %J Publications Mathématiques de l'IHÉS %D 2018 %P 219-397 %V 128 %I Springer Berlin Heidelberg %C Berlin/Heidelberg %U http://geodesic.mathdoc.fr/articles/10.1007/s10240-019-00102-z/ %R 10.1007/s10240-019-00102-z %G en %F PMIHES_2018__128__219_0
Bhatt, Bhargav; Morrow, Matthew; Scholze, Peter. Integral $p$-adic Hodge theory. Publications Mathématiques de l'IHÉS, Tome 128 (2018), pp. 219-397. doi: 10.1007/s10240-019-00102-z
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