论文标题
属属的Chow动机
Chow motives of genus one fibrations
论文作者
论文摘要
令$ f：x \ rightarrow c $是光滑的投影表面的属1元素，即其通用纤维是常规属1曲线。让$ J：J \ Rightarrow C $是$ F $的Jacobian纤维。在本文中，我们证明了$ x $和$ j $的Chow动机是同构的。作为一种应用，结合了我们在准纤维纤维动机上的伴随作品，我们证明了kimura的有限态度，用于平滑的投射表面，而不是一般类型，几何属属0。这概括了bloch-kas-kas-lieberman的结果。
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.
