Formal group laws in homotopy theory and K-theory

同伦理论和 K 理论中的形式群定律

• 批准号: 0805833
• 负责人: Tyler Lawson
• 金额: $ 12.8万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-06-01 至 2012-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0805833&HistoricalAwards=false
• 关键词: Formal; group; laws; homotopy; theory

AbstractAward: DMS-0805833Principal Investigator: Tyler D. LawsonThe goal of this project is to relate the theory of formal grouplaws to phenomena in stable homotopy theory and K-theory. Instable homotopy theory, the objective is to begin makingfundamental computations in the theory of topological automorphicforms developed in joint work with Behrens. This will firstproceed by examining and computing the homotopy of spectraassociated to certain moduli of abelian surfaces such as Shimuracurves, and then by working towards higher chromatic filtrations.In algebraic K-theory, the objective is to make systematic use ofthe relationship between formal group laws and complex cobordismto systematize computations in algebraic K-theory and relate themto the chromatic filtration, with the hope of gainingunderstanding of the "chromatic redshift" phenomenon.The subject of homotopy theory arose as a method to answerconcrete questions in geometry by way of algebra. In theprocess, a strange connection was discovered with formal grouplaws, which themselves are intimately related to quite differentsubjects such as number theory and elliptic curves. Inparticular, there is a surprising connection between ellipticcurves and mathematical physics. This research focuses onapplying very recent developments in homotopy theory to studyconnections such as these, with the hope that our understandingof number theory and our understanding of homotopy theory canbenefit each other.

Abstractaward：DMS-0805833原理研究者：Tyler D. Lawson这个项目的目标是将正式的Grouplaws理论与稳定同型理论和K理论中的现象联系起来。 目的是稳定的同义理论，是开始在与Behrens共同工作中开发的拓扑自动形态理论中进行基础计算。 首先，这将通过检查和计算与Abelian表面某些模量（如膜库库）的某些模量的同质性，然后通过努力朝着更高的色过滤器进行努力。在代数K理论中，目的是使系统法律与复杂的cobordations在Algebraic k-kneortation中的相关性和相关性相关的相关性与Algerbraic k-kneory的相关性相关性，并与之相关。获得“色度红移”现象的理解。同质理论的主题是一种通过代数来回答几何学问题的方法。 在过程中，与正式的grouplaws发现了一种奇怪的联系，这本身与数字理论和椭圆形曲线等非常不同的主体密切相关。 内部的，椭圆形和数学物理学之间存在令人惊讶的联系。 这项研究集中于同质理论中的最新发展，以此为类似的研究连接，希望我们的理解数理论和我们对同质理论的理解相互canbenefit。