Structural properties of equivariant and motivic stable homotopy categories

等变和动机稳定同伦范畴的结构性质

• 批准号: 203309416
• 负责人: Professor Dr. Jens Hornbostel
• 金额: --
• 依托单位: Arbeitsgruppe Topologie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2011
• 资助国家: 德国
• 起止时间: 2010-12-31 至 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/203309416?language=en
• 关键词: Structural; properties; equivariant; motivic; stable

We will study certain structural properties of the motivic stable homotopy category SH(k) over a given base field k as introduced by Morel and Voevodsky [MV], also called the stable A1-homotopy category. In particular, we wish to establish motivic generalizations of the famous classification results concerning thick subcategories as established by Hopkins and Smith [HS] within their work on nilpotence in stable homotopy. This would be a very big theorem, as so far there does not even exist a precise conjecture of how this classification might look like in the motivic case. What does exist are various suggestions for the construction of motivic versions of Morava K-theories, which in the classical case play a crucial role. As a first step, we wish to proceed towards a classification of thickideals in the G-equivariant stable homotopy category localized at a given prime p for some (e. g. finite cyclic) groups. There are some partial results in this direction (see below) due to Strickland [S2], which show that this certainly is a promising research project.

我们将研究Morel和Voevodsky [MV]在给定的基域k上引入的运动稳定同伦范畴SH（k）的某些结构性质，也称为稳定A1-同伦范畴。特别是，我们希望建立motivic推广的著名的分类结果，厚子范畴所建立的霍普金斯和史密斯[HS]在他们的工作中的零在稳定的同伦。这将是一个非常大的定理，因为到目前为止，甚至不存在一个精确的猜想，关于这种分类在动机的情况下可能是什么样子。对于摩拉瓦K理论的动机版本的构建，确实存在着各种各样的建议，在经典的情况下，这些建议起着至关重要的作用。作为第一步，我们希望对局部化于给定素数p的G-等变稳定同伦范畴中的厚理想进行分类，对于某些（e）。G.有限循环）群。由于Strickland [S2]，在这个方向上有一些部分结果（见下文），这表明这确实是一个有前途的研究项目。