Geodesic
Big de Rham-Witt cohomology: basic results
Documenta mathematica, Tome 19 (2014), pp. 567-599.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $X$ be a smooth projective $R$-scheme, where $R$ is a smooth $\Z$-algebra. As constructed by Hesselholt, we have the absolute big de Rham-Witt complex $\W\Omega^*_X$ of $X$ at our disposal. There is also a relative version $\W\Omega^*_{X/R}$ with $\W(R)$-linear differential. In this paper we study the hypercohomology of the relative (big) de Rham-Witt complex after truncation with finite truncation sets $S$. We show that it is a projective $\W_S(R)$-module, provided that the de Rham cohomology is a flat $R$-module. In addition, we establish a Poincaré duality theorem. explicit description of the relative de Rham-Witt complex of a smooth $\lambda$-ring, which may be of independent interest.
Classification : 14F40, 14F30 
@article{DOCMA_2014__19__a27,
     author = {Chatzistamatiou, Andre},
     title = {Big de {Rham-Witt} cohomology: basic results},
     journal = {Documenta mathematica},
     pages = {567--599},
     publisher = {mathdoc},
     volume = {19},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a27/}
}
TY  - JOUR
AU  - Chatzistamatiou, Andre
TI  - Big de Rham-Witt cohomology: basic results
JO  - Documenta mathematica
PY  - 2014
SP  - 567
EP  - 599
VL  - 19
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a27/
LA  - en
ID  - DOCMA_2014__19__a27
ER  - 
%0 Journal Article
%A Chatzistamatiou, Andre
%T Big de Rham-Witt cohomology: basic results
%J Documenta mathematica
%D 2014
%P 567-599
%V 19
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a27/
%G en
%F DOCMA_2014__19__a27
Chatzistamatiou, Andre. Big de Rham-Witt cohomology: basic results. Documenta mathematica, Tome 19 (2014), pp. 567-599. http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a27/