模型中的主要理想- $\ell $米尔诺k理论

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2017-05-12 DOI:10.1007/s40062-017-0176-0

Charles Weibel, Inna Zakharevich

{"title":"模型中的主要理想- \$\\ell \$米尔诺k理论","authors":"Charles Weibel, Inna Zakharevich","doi":"10.1007/s40062-017-0176-0","DOIUrl":null,"url":null,"abstract":"Fix a symbol \$\\underline{a}\$ in the mod-\$\\ell \$ Milnor K-theory of a field k, and a norm variety X for \$\\underline{a}\$. We show that the ideal generated by \$\\underline{a}\$ is the kernel of the K-theory map induced by \$k\\subset k(X)\$ and give generators for the annihilator of the ideal. When \$\\ell =2\$, this was done by Orlov, Vishik and Voevodsky.","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"12 4","pages":"1033 - 1049"},"PeriodicalIF":0.5000,"publicationDate":"2017-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-017-0176-0","citationCount":"1","resultStr":"{\"title\":\"Principal ideals in mod-\\\$\\\\ell \\\$ Milnor K-theory\",\"authors\":\"Charles Weibel, Inna Zakharevich\",\"doi\":\"10.1007/s40062-017-0176-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Fix a symbol \\\$\\\\underline{a}\\\$ in the mod-\\\$\\\\ell \\\$ Milnor K-theory of a field k, and a norm variety X for \\\$\\\\underline{a}\\\$. We show that the ideal generated by \\\$\\\\underline{a}\\\$ is the kernel of the K-theory map induced by \\\$k\\\\subset k(X)\\\$ and give generators for the annihilator of the ideal. When \\\$\\\\ell =2\\\$, this was done by Orlov, Vishik and Voevodsky.\",\"PeriodicalId\":636,\"journal\":{\"name\":\"Journal of Homotopy and Related Structures\",\"volume\":\"12 4\",\"pages\":\"1033 - 1049\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2017-05-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s40062-017-0176-0\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Homotopy and Related Structures\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-017-0176-0\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Homotopy and Related Structures","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40062-017-0176-0","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 1

摘要

修正了一个符号$\underline{a}$在mod- $\ell $米尔诺k理论的一个字段k，和一个范数变种X的$\underline{a}$。我们证明了$\underline{a}$产生的理想是$k\subset k(X)$诱导的k理论映射的核，并给出了理想湮灭子的产生器。当$\ell =2$，这是由Orlov, Vishik和Voevodsky完成的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$Principal ideals in mod-$\ell $ Milnor K-theory$

查看原文本刊更多论文

Principal ideals in mod-$\ell $ Milnor K-theory

Fix a symbol $\underline{a}$ in the mod-$\ell $ Milnor K-theory of a field k, and a norm variety X for $\underline{a}$. We show that the ideal generated by $\underline{a}$ is the kernel of the K-theory map induced by $k\subset k(X)$ and give generators for the annihilator of the ideal. When $\ell =2$, this was done by Orlov, Vishik and Voevodsky.

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

来源期刊

Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

自引率

0.00%

发文量

期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.

模型中的主要理想- \(\ell \)米尔诺k理论

摘要