Big de Rham-Witt cohomology: basic results

Andre Chatzistamatiou

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arXiv · 1211.6006

Big de Rham-Witt cohomology: basic results

Andre Chatzistamatiou

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Abstract

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 Poincar\'e duality theorem.

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BibTeX RIS

Andre Chatzistamatiou. 2012-11-26. Big de Rham-Witt cohomology: basic results. https://arxiv.org/abs/1211.6006

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