K-theories, Cycle Theories, and Cohomology Calculations

K 理论、循环理论和上同调计算

• 批准号: 9988130
• 负责人: Eric Friedlander
• 金额: $ 18.54万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-06-15 至 2004-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9988130&HistoricalAwards=false
• 关键词: theories; Cycle; Theories; Cohomology; Calculations

Friedlander-Abstract The relationship between algebraic K-theory and algebraic cycles is of fundamental importance. Friedlander proposes to consider his investigations of this relationship by continuing to contemplate the spectral sequence developed in collaboration with Suslin and by studying Chern classes to various cohomology theories. Much of Friedlander's effort will be directed to semi-topological K-theory (being developed in collaboration with Mark Walker) and its relationship with morphic cohomology (developed in collaboration with Blaine Lawson). Friedlander also proposes to further investigate the representation theory of algebras related to algebraic groups, in part through the thesis work of several Ph.D. students.Throughout the twentieth century, algebraic topology (mathematics of "bending and twisting") and algebraic geometry (mathematics of "surfaces" coming from graphing polynomial equations) enjoyed a very positive interactive relationship. The types of geometric objects ("surfaces") studied by topologists can be more general than geometric "surfaces" called algebraic varieties, but many of the most basic and interesting topological "surfaces" are algebraic varieties. Constructions and techniques arising naturally in either geometry or topology continue to be successfully imported to the other area, often with surprising computational or conceptual results. Much of the proposed work is to use techniques and to pose questions that are topological in character to gain a better understanding of some central aspects of algebraic geometry.

弗里德兰德（Friedlander）取消代数K理论与代数周期之间的关系至关重要。 弗里德兰德（Friedlander）建议通过继续考虑与苏斯林（Suslin）合作开发的光谱序列，并通过研究各种共同体理论的Chern类，来考虑他对这种关系的调查。 弗里德兰德（Friedlander）的大部分努力都将针对半流行病理论（与马克·沃克（Mark Walker）合作开发）及其与形态同谋的关系（与布莱恩·劳森（Blaine Lawson）合作开发）。 弗里德兰德（Friedlander）还建议进一步研究与代数群体相关的代数的表示理论，部分是通过多个博士学位的论文工作。学生。到20世纪，代数拓扑（“弯曲和扭曲”的数学）和代数几何（来自绘制多项式方程的“表面”的数学）具有非常积极的互动关系。 拓扑师研究的几何对象（“表面”）的类型比几何“表面”更一般，称为代数品种，但是许多最基本和有趣的拓扑“表面”是代数品种。 在几何或拓扑中自然产生的结构和技术继续成功地进口到其他领域，通常会带有令人惊讶的计算或概念结果。 拟议的许多工作是使用技术并提出拓扑特征的问题，以更好地了解代数几何的某些中心方面。