Lectures on Algebraic Cycles and Chow Groups

Abstract

This chapter showcases five lectures on algebraic cycles and Chow groups. The first two lectures are over an arbitrary field, where they examine algebraic cycles, Chow groups, and equivalence relations. The second lecture also offers a short survey on the results for divisors. The next two lectures are over the complex numbers. The first of these features discussions on the cycle map, the intermediate Jacobian, Abel–Jacobi map, and the Deligne cohomology. The following lecture focuses on algebraic versus homological equivalence, as well as the Griffiths group. The final lecture, which returns to the arbitrary field, discusses the Albanese kernel and provides the results of Mumford, Bloch, and Bloch–Srinivas.