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Big de Rham-Witt cohomology: basic results | | Andre Chatzistamatiou
; | | Date: |
26 Nov 2012 | | Abstract: | Let $X$ be a smooth projective $R$-scheme, and let $R$ be an ’etale
$$-algebra. As constructed by Hesselholt, we have the absolute big de
Rham-Witt complex $WOmega^*_X$ of $X$ at our disposal. There is also a
relative version $WOmega^*_{X/}$ that is characterized by the vanishing of
the positive degree part in the case $X=Spec()$. In this paper we study the
hypercohomology of the relative (big) de Rham-Witt complex of $X$. We show that
it is a projective module over the ring of (big) Witt vectors of $R$, provided
that the de Rham cohomology is torsion-free. In addition, we establish a
Poincar’e duality theorem. Our results rely on an explicit description of the
relative de Rham-Witt complex of a smooth $lambda$-ring, which may be of
independent interest. | | Source: | arXiv, 1211.6006 | | Services: | Forum | Review | PDF | Favorites | |
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