Algebraic cycles on homogeneous varieties

同质簇上的代数循环

• 批准号: 385795-2010
• 负责人: Zaynullin, Kirill
• 金额: $ 1.89万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508808
• 关键词: Algebraic; cycles; homogeneous; varieties

Cohomological methods in mathematics were introduced and applied in the middle of the last century by Solomon Lefschetz to study complex algebraic varieties. During the next decade they were essentially developed by Andre Weil and Alexander Grothendieck leading to the proof of the famous Weil's Conjectures by Pierre Deligne. Since then cohomological methods have become a fundamental technique in mathematics which in many cases led to the resolution of classical algebraic and geometric problems. Among the major recent achievements in this direction one should mention: the oriented cohomology theory, the theory of algebraic cobordism by Levine-Morel and the theory of motives by Grothendieck, Manin and Voevodsky. Another central object of the modern mathematics is the notion of a (linear algebraic) group G acting on a variety or manifold X. The basic example is the group of linear transformations acting on a vector space. The geometry of G and X has been a subject of intensive investigations for almost a century, with important contributions by Armand Borel, Claude Chevalley, Michel Demazure, Jean-Pierre Serre, Jaques Tits, and others.

数学中的上同调方法由所罗门·莱夫谢茨 (Solomon Lefschetz) 在上世纪中叶引入并应用来研究复杂的代数簇。在接下来的十年里，它们基本上是由安德烈·韦尔和亚历山大·格洛腾迪克发展起来的，最终由皮埃尔·德利涅证明了著名的韦尔猜想。从那时起，上同调方法已成为数学中的一项基本技术，在许多情况下导致了经典代数和几何问题的解决。在这一方向最近取得的主要成就中，值得一提的是：有向上同调理论、Levine-Morel 的代数共边理论以及 Grothendieck、Manin 和 Voevodsky 的动机理论。现代数学的另一个中心对象是作用于变量或流形 X 的（线性代数）群 G 的概念。基本的例子是作用于向量空间的线性变换群。近一个世纪以来，G 和 X 的几何形状一直是深入研究的课题，Armand Borel、Claude Chevalley、Michel Demazure、Jean-Pierre Serre、Jaques Tits 等人做出了重要贡献。