{"title":"属一纤维的周动机","authors":"Daiki Kawabe","doi":"10.1007/s00229-024-01557-z","DOIUrl":null,"url":null,"abstract":"<p>Let <span>\\(f: X \\rightarrow C\\)</span> be a genus 1 fibration from a smooth projective surface, i.e. its generic fiber is a regular genus 1 curve. Let <span>\\(j: J \\rightarrow C\\)</span> be the Jacobian fibration of <i>f</i>. In this paper, we prove that the Chow motives of <i>X</i> and <i>J</i> 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.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Chow motives of genus one fibrations\",\"authors\":\"Daiki Kawabe\",\"doi\":\"10.1007/s00229-024-01557-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <span>\\\\(f: X \\\\rightarrow C\\\\)</span> be a genus 1 fibration from a smooth projective surface, i.e. its generic fiber is a regular genus 1 curve. Let <span>\\\\(j: J \\\\rightarrow C\\\\)</span> be the Jacobian fibration of <i>f</i>. In this paper, we prove that the Chow motives of <i>X</i> and <i>J</i> 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.\\n</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-04-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00229-024-01557-z\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00229-024-01557-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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。
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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