有限域上阿贝尔变的自积上的泰特类

Pub Date : 2020-05-09 DOI:10.5802/aif.3483

Y. Zarhin

{"title":"有限域上阿贝尔变的自积上的泰特类","authors":"Y. Zarhin","doi":"10.5802/aif.3483","DOIUrl":null,"url":null,"abstract":"We deal with $g$-dimensional abelian varieties $X$ over finite fields. We prove that there is an universal constant (positive integer) $N=N(g)$ that depends only on $g$ that enjoys the following properties. If a certain self-product of $X$ carries an exotic Tate class then the self-product $X^{2N}$of $X$ also carries an exotic Tate class. This gives a positive answer to a question of Kiran Kedlaya.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Tate classes on self-products of Abelian varieties over finite fields\",\"authors\":\"Y. Zarhin\",\"doi\":\"10.5802/aif.3483\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We deal with $g$-dimensional abelian varieties $X$ over finite fields. We prove that there is an universal constant (positive integer) $N=N(g)$ that depends only on $g$ that enjoys the following properties. If a certain self-product of $X$ carries an exotic Tate class then the self-product $X^{2N}$of $X$ also carries an exotic Tate class. This gives a positive answer to a question of Kiran Kedlaya.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2020-05-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5802/aif.3483\",\"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/10.5802/aif.3483","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 1

摘要

我们处理有限域上的$g$维阿贝尔变量$X$。我们证明了存在一个仅依赖于$g$的普适常数(正整数)$ N=N(g)$，它具有下列性质。如果$X$的某个自积$X$携带一个奇异的Tate类，那么$X$的自积$X^{2N}$也携带一个奇异的Tate类。这对Kiran Kedlaya的问题给出了肯定的回答。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

Tate classes on self-products of Abelian varieties over finite fields

We deal with $g$-dimensional abelian varieties $X$ over finite fields. We prove that there is an universal constant (positive integer) $N=N(g)$ that depends only on $g$ that enjoys the following properties. If a certain self-product of $X$ carries an exotic Tate class then the self-product $X^{2N}$of $X$ also carries an exotic Tate class. This gives a positive answer to a question of Kiran Kedlaya.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助