拆分米尔诺-维特动机及其在纤维束中的应用

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-11-02 DOI:10.4310/cjm.2022.v10.n4.a5

N. Yang

{"title":"拆分米尔诺-维特动机及其在纤维束中的应用","authors":"N. Yang","doi":"10.4310/cjm.2022.v10.n4.a5","DOIUrl":null,"url":null,"abstract":". We study the Milnor-Witt motives which are a ﬁnite direct sum of Z ( q )[ p ] and Z /η ( q )[ p ]. We show that for MW-motives of this type, we can determine an MW-motivic cohomology class in terms of a motivic cohomology class and a Witt cohomology class. We deﬁne the motivic Bockstein cohomology and show that it corresponds to subgroups of Witt cohomology, if the MW-motive splits as above. As an application, we give the splitting formula of Milnor-Witt motives of Grassmannian bundles and complete ﬂag bundles. This in particular shows that the integral cohomology of real complete ﬂags has only 2-torsions.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Split Milnor–Witt motives and its applications to fiber bundles\",\"authors\":\"N. Yang\",\"doi\":\"10.4310/cjm.2022.v10.n4.a5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We study the Milnor-Witt motives which are a ﬁnite direct sum of Z ( q )[ p ] and Z /η ( q )[ p ]. We show that for MW-motives of this type, we can determine an MW-motivic cohomology class in terms of a motivic cohomology class and a Witt cohomology class. We deﬁne the motivic Bockstein cohomology and show that it corresponds to subgroups of Witt cohomology, if the MW-motive splits as above. As an application, we give the splitting formula of Milnor-Witt motives of Grassmannian bundles and complete ﬂag bundles. This in particular shows that the integral cohomology of real complete ﬂags has only 2-torsions.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2020-11-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/cjm.2022.v10.n4.a5\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cjm.2022.v10.n4.a5","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 1

摘要

.我们研究了Milnor-Witt动机，它是Z（q）[p]和Z/η（q）[p]的有限直和。我们证明了对于这种类型的MW动机，我们可以根据一个动机上同调类和一个Witt上同调类别来确定一个MW动机上同同调类别。我们定义了动机Bockstein上同调，并证明它对应于Witt上同调的子群，如果MW动机如上所述分裂。作为一个应用，我们给出了Grassmannian丛和完备fleag丛的Milnor-Witt动机的分裂公式。这特别表明，实完全函数的积分上同调只有2-扭转。

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

Split Milnor–Witt motives and its applications to fiber bundles

. We study the Milnor-Witt motives which are a ﬁnite direct sum of Z ( q )[ p ] and Z /η ( q )[ p ]. We show that for MW-motives of this type, we can determine an MW-motivic cohomology class in terms of a motivic cohomology class and a Witt cohomology class. We deﬁne the motivic Bockstein cohomology and show that it corresponds to subgroups of Witt cohomology, if the MW-motive splits as above. As an application, we give the splitting formula of Milnor-Witt motives of Grassmannian bundles and complete ﬂag bundles. This in particular shows that the integral cohomology of real complete ﬂags has only 2-torsions.

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.