Avery Ching, HKUST, Hong Kong

A proposed filtration of Chow groups

The Chow groups of varieties are studied by the cycle class map and the Abel Jacobi map. But certain parts of Chow groups are much more complicated and they cannot be studied by these two maps. They are supposed to be given by the existence of a conjectural filtration. In this talk, we will describe a proposed filtration given by P. Griffiths and discuss the shortcoming for such a construction. We will also see some problems solved by this method and some open problems which are potentially done in this way.