Split Milnor–Witt motives and its applications to fiber bundles

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

引用次数: 1

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.

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拆分米尔诺-维特动机及其在纤维束中的应用

.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。

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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

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