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- W4300485863 abstract "Let $k$ be a field and let $Omega$ be a universal domain over $k$. Let $f:X r S$ be a dominant morphism defined over $k$ from a smooth projective variety $X$ to a smooth projective variety $S$ of dimension $leq 2$ such that the general fibre of $f_Omega$ has trivial Chow group of zero-cycles. For example, $X$ could be the total space of a two-dimensional family of varieties whose general member is rationally connected. Suppose that $X$ has dimension $leq 4$. Then we prove that $X$ has a self-dual Murre decomposition, i.e. that $X$ has a self-dual Chow--Kuenneth decomposition which satisfies Murre's conjectures (B) and (D). Moreover we prove that the motivic Lefschetz conjecture holds for $X$ and hence so does the Lefschetz standard conjecture. We also give new examples of threefolds of general type which are Kimura finite-dimensional, new examples of fourfolds of general type having a self-dual Murre decomposition, as well as new examples of varieties with finite degree three unramified cohomology." @default.
- W4300485863 created "2022-10-03" @default.
- W4300485863 creator A5089099792 @default.
- W4300485863 date "2011-11-15" @default.
- W4300485863 modified "2023-09-26" @default.
- W4300485863 title "Chow-Kuenneth decomposition for 3- and 4-folds fibred by varieties with small Chow group of zero-cycles" @default.
- W4300485863 doi "https://doi.org/10.48550/arxiv.1111.3658" @default.
- W4300485863 hasPublicationYear "2011" @default.
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