Oriented cohomology theories and equivariant motives
定向上同调理论和等变模体
基本信息
- 批准号:268769163
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:德国
- 项目类别:Priority Programmes
- 财政年份:2015
- 资助国家:德国
- 起止时间:2014-12-31 至 2020-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The concept of an oriented cohomology theory is well known in algebraic topology. In algebraic geometry it was introduced and systematically studied by Levine, Morel, Panin and Smirnov. Moreover, there exist an equivariant version of oriented cohomology theories. Similar to Grothendieck's construction of Chow motives, one can define the category of motives with respect to any oriented cohomology theory (ordinary or equivariant). Motives play a central role in understanding of the cohomologies of schemes and in the algebraic geometry by itself. There exists a broad literature devoted to classical Chow motives (also due to the applicant), but so far there are very few results about the structure of motives with respect to arbitrary oriented cohomology theories. To make progress on this is one of the goals of the present project.
定向上同调理论的概念在代数拓扑学中是众所周知的。在代数几何介绍和系统研究了莱文,莫雷尔,潘宁和斯米尔诺夫。此外,有向上同调理论存在一个等变版本。类似于格罗滕迪克的周动机的构造,人们可以定义关于任何定向上同调理论(普通或等变)的动机类别。动机在理解图式的上同调和代数几何本身中起着核心作用。有大量的文献致力于经典的Chow动机(也是由于申请人),但到目前为止,关于任意定向上同调理论的动机结构的结果很少。在这方面取得进展是本项目的目标之一。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Professor Dr. Nikita Geldhauser其他文献
Professor Dr. Nikita Geldhauser的其他文献
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{{ truncateString('Professor Dr. Nikita Geldhauser', 18)}}的其他基金
Algebraic groups and motives of projective homogeneous varieties of outer type
外型射影齐次簇的代数群和母题
- 批准号:
432236229 - 财政年份:
- 资助金额:
-- - 项目类别:
Research Grants
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