属一纤维的周动机

IF 0.5 4区数学 Q3 MATHEMATICS

Manuscripta Mathematica Pub Date : 2024-04-21 DOI:10.1007/s00229-024-01557-z

Daiki Kawabe

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引用次数: 0

摘要

让 \(f: X \rightarrow C\) 是来自光滑投影面的属 1 纤维，即它的一般纤维是规则的属 1 曲线。让 \(j: J \rightarrow C\) 是 f 的雅各布纤维。在本文中，我们将证明 X 和 J 的周动机是同构的。作为应用，结合我们对准椭圆纤度的动机的研究，我们证明了几何属数为 0 的非一般类型光滑投影面的木村有限维性（Kimura finite-dimensionality），这将布洛赫-卡斯-利伯曼（Bloch-Kas-Lieberman）的结果推广到了任意特性。

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Chow motives of genus one fibrations

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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来源期刊

Manuscripta Mathematica 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： manuscripta mathematica was founded in 1969 to provide a forum for the rapid communication of advances in mathematical research. Edited by an international board whose members represent a wide spectrum of research interests, manuscripta mathematica is now recognized as a leading source of information on the latest mathematical results.