Big de Rham-Witt cohomology: basic results
Andre Chatzistamatiou
Fachbereich Mathematik Universität Duisburg-Essen 45117 Essen Germany
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Abstract
Let be a smooth projective -scheme, where is a smooth -algebra. As constructed by Hesselholt, we have the absolute big de Rham–Witt complex of at our disposal. There is also a relative version with -linear differential. In this paper we study the hypercohomology of the relative (big) de Rham-Witt complex after truncation with finite truncation sets . We show that it is a projective -module, provided that the de Rham cohomology is a flat -module. In addition, we establish a Poincaré duality theorem. explicit description of the relative de Rham–Witt complex of a smooth -ring, which may be of independent interest.
Cite this article
Andre Chatzistamatiou, Big de Rham-Witt cohomology: basic results. Doc. Math. 19 (2014), pp. 567–599
DOI 10.4171/DM/456