Geodesic
Article
Topological Hochschild homology and integral p-adic Hodge theory
Publications Mathématiques de l'IHÉS, Tome 129 (2019), pp. 199-310

Voir la notice de l'article provenant de la source Numdam

In mixed characteristic and in equal characteristic p we define a filtration on topological Hochschild homology and its variants. This filtration is an analogue of the filtration of algebraic K-theory by motivic cohomology. Its graded pieces are related in mixed characteristic to the complex AΩ constructed in our previous work, and in equal characteristic p to crystalline cohomology. Our construction of the filtration on THH is via flat descent to semiperfectoid rings.

As one application, we refine the construction of the AΩ-complex by giving a cohomological construction of Breuil–Kisin modules for proper smooth formal schemes over 𝒪 K , where K is a discretely valued extension of 𝐐 p with perfect residue field. As another application, we define syntomic sheaves 𝐙 p (n) for all n≥0 on a large class of 𝐙 p -algebras, and identify them in terms of p-adic nearby cycles in mixed characteristic, and in terms of logarithmic de Rham-Witt sheaves in equal characteristic p.

Reçu le :
Accepté le :
Première publication :
Publié le :
DOI : 10.1007/s10240-019-00106-9

Bhatt, Bhargav 1 ; Morrow, Matthew  ; Scholze, Peter 

1 
@article{PMIHES_2019__129__199_0,
     author = {Bhatt, Bhargav and Morrow, Matthew and Scholze, Peter},
     title = {Topological {Hochschild} homology and integral $p$-adic {Hodge} theory},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {199--310},
     publisher = {Springer Berlin Heidelberg},
     address = {Berlin/Heidelberg},
     volume = {129},
     year = {2019},
     doi = {10.1007/s10240-019-00106-9},
     mrnumber = {3949030},
     zbl = {1478.14039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-019-00106-9/}
}
TY  - JOUR
AU  - Bhatt, Bhargav
AU  - Morrow, Matthew
AU  - Scholze, Peter
TI  - Topological Hochschild homology and integral $p$-adic Hodge theory
JO  - Publications Mathématiques de l'IHÉS
PY  - 2019
SP  - 199
EP  - 310
VL  - 129
PB  - Springer Berlin Heidelberg
PP  - Berlin/Heidelberg
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10240-019-00106-9/
DO  - 10.1007/s10240-019-00106-9
LA  - en
ID  - PMIHES_2019__129__199_0
ER  - 
%0 Journal Article
%A Bhatt, Bhargav
%A Morrow, Matthew
%A Scholze, Peter
%T Topological Hochschild homology and integral $p$-adic Hodge theory
%J Publications Mathématiques de l'IHÉS
%D 2019
%P 199-310
%V 129
%I Springer Berlin Heidelberg
%C Berlin/Heidelberg
%U http://geodesic.mathdoc.fr/articles/10.1007/s10240-019-00106-9/
%R 10.1007/s10240-019-00106-9
%G en
%F PMIHES_2019__129__199_0
Bhatt, Bhargav; Morrow, Matthew; Scholze, Peter. Topological Hochschild homology and integral $p$-adic Hodge theory. Publications Mathématiques de l'IHÉS, Tome 129 (2019), pp. 199-310. doi: 10.1007/s10240-019-00106-9

Cité par Sources :