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arXiv · 2201.06162

Chow motives of genus one fibrations

Daiki Kawabe
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Abstract

Let $f: X \rightarrow C$ be a genus 1 fibration from a smooth projective surface, i.e. its generic fiber is a regular genus 1 curve. Let $j: J \rightarrow C$ be the Jacobian fibration of $f$. In this paper, we prove that the Chow motives of $X$ and $J$ are isomorphic. As an application, combined with our concomitant work on motives of quasi-elliptic fibrations, we prove Kimura finite-dimensionality for smooth projective surfaces not of general type with geometric genus 0. This generalizes Bloch-Kas-Lieberman's result to arbitrary characteristic.

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Daiki Kawabe. 2022-01-17. Chow motives of genus one fibrations. https://doi.org/10.1007/s00229-024-01557-z

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