Enriched motivic homotopy theory

丰富的动机同伦理论

• 批准号: EP/J013064/1
• 负责人: Grigory Garkusha
• 金额: $ 2.83万
• 依托单位: Swansea University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2012
• 资助国家: 英国
• 起止时间: 2012 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FJ013064%2F1
• 关键词: Enriched; motivic; homotopy; theory

The versatility of motivic homotopy theory and its associated range of cohomological techniques has made it an important branch of mathematics. Recently there have been several fundamental developments which have been used to solve a number of longstanding problems. The new strategically important developments are related to the names of V. Voevodsky (Fields Medal 2002), M. Rost, A. Suslin, I. Panin, M. Levine, F. Morel.The principal aim of this project is to investigate enriched motivic homotopy theory. It is hoped that its study will shed light on some classical problems in A^1-topology. We propose to use its methods to construct various triangulated categories of motives, one of the central objects of study in modern A^1-topology. We believe that these constructions will have important computational advantages. The homotopy-theoretic outlook that we develop is likely to be useful in other areas of mathematics such as algebraic topology and non-commutative geometry.The research will be undertaken in the Department of Mathematics, Swansea University.

动机同质理论及其相关的共同体技术范围的多功能性使其成为数学的重要组成部分。最近，已经有一些基本发展，这些发展已用于解决许多长期存在的问题。新的战略性重要的发展与V. Voevodsky的名称有关（Fields Medal 2002），M。Rost，A。Suslin，I。Panin，M。Levine，F。Morel。该项目的主要目的是研究富集的动机同型理论。希望它的研究能够阐明^1-Topology中的一些经典问题。我们建议使用其方法来构建各种三角类别的动机类别，这是现代A^1-Topology中研究的中心对象之一。我们认为这些结构将具有重要的计算优势。我们开发的同质理论前景可能在数学的其他领域（例如代数拓扑和非共同的几何学）中有用。该研究将在斯旺西大学数学系进行。

项目成果

ON THE MOTIVIC SPECTRAL SEQUENCE

关于动机谱序列

• DOI: 10.1017/s1474748015000419
• 发表时间: 2015
• 期刊: Journal of the Institute of Mathematics of Jussieu
• 影响因子: 0.9
• 作者: Garkusha G