Algebraic cycles and motivic cohomology

代数环和动机上同调

• 批准号: 341288-2007
• 负责人: Rosenschon, Andreas
• 金额: $ 0.28万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=366214
• 关键词: Algebraic; cycles; motivic; cohomology

This research proposal is concerned with various questions resulting from the recent progress in the study of `motives'. These are mathematical objects which were introduced by Grothendieck and Manin in the 1960's, initially, to unify several cohomolog theories and to study a long-standing conjecture by Weil. Over the years it has become clear that motives have many applications in different branches of mathematics, for example, algebraic geometry, topology, number theory and representation theory. In fact, it turned out that the language of motives provides a common framework in which many fundamental problems in different branches of mathematics can be explained. Whereas for a long time the theory of motives was largely conjectural, in recent years there has been dramatic progress in making this theory precise. These developments created new theories as well as powerful computational tools. In this proposal we address theoretical and concrete computational questions whose resolution would significantly improve our understanding of this fundamental theory.

本研究计划涉及“动机”研究的最新进展所产生的各种问题。这些数学对象由 Grothendieck 和 Manin 在 1960 年代引入，最初是为了统一几种上同调理论并研究 Weil 的一个长期存在的猜想。多年来，人们已经清楚动机在数学的不同分支中有许多应用，例如代数几何、拓扑、数论和表示论。事实上，事实证明，动机语言提供了一个共同的框架，可以在其中解释不同数学分支的许多基本问题。长期以来，动机理论主要是推测性的，但近年来，在使这一理论更加精确方面取得了巨大进展。这些发展创造了新的理论和强大的计算工具。在这个提案中，我们解决了理论和具体的计算问题，这些问题的解决将显着提高我们对这一基本理论的理解。