米尔诺-维特动机同调与线性代数群

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-18 DOI:10.1016/j.aim.2024.109973

Keyao Peng

引用次数: 0

摘要

本文介绍了 MW 动同调的两个关键计算。首先，对于任意 n∈N 的交映群 Sp2n，我们利用 Sp 方向和相关的伯勒类计算其 MW 动同调。其次，我们按照经典计算方法，利用李雷谱序列在 A1-同调中的类比，计算了一般 Stiefel varieties 的 η-反转 MW-动同调，特别是计算了一般线性群 GLn 和特殊线性群 SLn 对于任意 n∈N 的 η-反转 MW-动同调。

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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Milnor-Witt motivic cohomology and linear algebraic groups

This article presents two key computations in MW-motivic cohomology. Firstly, we compute the MW-motivic cohomology of the symplectic groups

{Sp}_{2 n}

for any

n \in N

using the Sp-orientation and the associated Borel classes.

Secondly, following the classical computations and using the analogue in

A^{1}

-homotopy of the Leray spectral sequence, we compute the η-inverted MW-motivic cohomology of general Stiefel varieties, obtaining in particular the computation of the η-inverted MW-motivic cohomology of the general linear groups

{GL}_{n}

and the special linear groups

{SL}_{n}

for any

n \in N

Finally, we determine the multiplicative structures of these total cohomology groups.

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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

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.