报告题目: Lectures on the higher Abel-Jacobi map
报告人: Thomas Weissschuh, University of Mainz
摘要: In the first lecture, higher Chow groups are discussed together with some complexes which can be used to compute them. Normalized and alternating chains are introduced and the intersection product on these complexes is defined. The second (and maybe part of the third) lecture threads Deligne-Beilinson cohomology. It starts with a short introduction to the notion of currents on manifolds, which is then used to define a complex C for the Deligne-Beilinson cohomology. Finally, a second complex P is introduced, and its relation to the previous complex is discussed. In the remaining time, we explain how to define maps from higher Chow chains to the complexes C and P and examine some of their properties. These maps give rise to Abel-Jacobi maps for higher Chow groups. We define them and give explicit formulas.