具有规定约简行为的Severi-Brauer变种的代数连接K理论

IF 0.9 3区数学 Q2 MATHEMATICS

Documenta Mathematica Pub Date : 2021-01-01 DOI:10.4171/dm/820

Eoin Mackall

{"title":"具有规定约简行为的Severi-Brauer变种的代数连接K理论","authors":"Eoin Mackall","doi":"10.4171/dm/820","DOIUrl":null,"url":null,"abstract":"We show that Chow groups of low dimension cycles are torsion free for a class of sufficiently generic Severi-Brauer varieties. Using a recent result of Karpenko, this allows us to compute the algebraic connective K-theory in low degrees for the same class of varieties. Independently of these results, we show that the associated graded ring for the topological filtration on the Grothendieck ring is torsion free in the same degrees for arbitrary SeveriBrauer varieties.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Algebraic connective $K$-theory of a Severi-Brauer variety with prescribed reduced behavior\",\"authors\":\"Eoin Mackall\",\"doi\":\"10.4171/dm/820\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that Chow groups of low dimension cycles are torsion free for a class of sufficiently generic Severi-Brauer varieties. Using a recent result of Karpenko, this allows us to compute the algebraic connective K-theory in low degrees for the same class of varieties. Independently of these results, we show that the associated graded ring for the topological filtration on the Grothendieck ring is torsion free in the same degrees for arbitrary SeveriBrauer varieties.\",\"PeriodicalId\":50567,\"journal\":{\"name\":\"Documenta Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Documenta Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/dm/820\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Documenta Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/dm/820","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

我们证明了低维环的Chow群对于一类充分泛型的Severi-Brauer变体是无扭转的。利用Karpenko最近的一个结果，这允许我们在低阶上计算相同种类的代数连接k理论。独立于这些结果，我们证明了格罗登狄克环上的拓扑过滤的相关梯度环对于任意的SeveriBrauer变体在相同程度上是无扭转的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Algebraic connective $K$-theory of a Severi-Brauer variety with prescribed reduced behavior

We show that Chow groups of low dimension cycles are torsion free for a class of sufficiently generic Severi-Brauer varieties. Using a recent result of Karpenko, this allows us to compute the algebraic connective K-theory in low degrees for the same class of varieties. Independently of these results, we show that the associated graded ring for the topological filtration on the Grothendieck ring is torsion free in the same degrees for arbitrary SeveriBrauer varieties.

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

Documenta Mathematica 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： DOCUMENTA MATHEMATICA is open to all mathematical fields und internationally oriented Documenta Mathematica publishes excellent and carefully refereed articles of general interest, which preferably should rely only on refereed sources and references.