Geodesic
Big de Rham-Witt cohomology: basic results
Documenta mathematica, Tome 19 (2014), pp. 567-599
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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 WΩX∗​ of X at our disposal. There is also a relative version WΩX/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 WS​(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 λ-ring, which may be of independent interest.
DOI : 10.4171/dm/456
Classification : 14F30, 14F40 
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     author = {Andre Chatzistamatiou},
     title = {Big de {Rham-Witt} cohomology: basic results},
     journal = {Documenta mathematica},
     pages = {567--599},
     year = {2014},
     volume = {19},
     doi = {10.4171/dm/456},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/456/}
}
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Andre Chatzistamatiou. Big de Rham-Witt cohomology: basic results. Documenta mathematica, Tome 19 (2014), pp. 567-599. doi: 10.4171/dm/456

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