Seminar

In this lecture, I will discuss aspects of the study of algebraic cycles, in relation to the Grothendieck group of vector bundles, on algebraic varieties with singularities. I will first briefly review the non-singular case, and make an analogy with topology. Then I will explain some things we know, in analogy with the non-singular case, point out the (wide) gaps in our understanding, and explain some results and examples. In some cases, these give evidence supporting conjectures which are difficult open questions even in the smooth case (Bloch and Bloch-Beilinson Conjectures). In other cases, we encounter phenomena in the singular case which are perhaps counter-intuitive.