关于 Abel 簇和广义 Kummer 簇的 Chow 群的研究

代数闭链理论是代数几何中的最重要的领域之一，其中包括 Hodge 猜想，它是千禧年七大问题之一。本项目主要研究代数闭链理论中的几个问题,，即：关于 Abel 簇和广义 Kummer 簇的 Chow 群的结构和性质问题。. (1) 研究关于任意 Abel 簇上余-2-维 Chow 群的 Bloch-Beilinson-Murre 猜想；. (2) 研究广义 Kummer 簇的 Chow 群的分裂性；. (3) 研究广义 Kummer 簇的代数上同调环的典范 Chow-提升性。

The theory of algebraic cycles is most important in algebraic geometry, which contains the Hodge conjecture, one of the seven problems for the Clay Millinnium Prize. This program focuses on several questions in the theory of algebraic cycles, namely, the structure and properties of the Chow groups of abelian varieties and generalized Kummer varieties.. (1) The Bloch-Beilinson-Murre conjecture for the codimension-2 Chow groups of abelian varieties is concerned;. (2) It will be made clear whether the Chow groups of generalized Kummer varieties are split.. (3) It will determined whether the algebraic cohomology rings of generalized Kummer varieties admit canonical Chow-liftings.