Souvik Goswami, Texas A&M University
3:30 pm, Friday, April 26, TUC 243
Abstract: For a smooth and projective variety defined over a number field, Beilinson attached the notion of height pairing to two algebraic cycles homologous to zero, and in complimentary codimensions. This pairing has two components, the non-archimedean one – for finite primes of the number field, and the other archimedean, arising from the embeddings of the number field inside the complex number field. The archimedean part of the height pairing can be defined independently for any smooth projective and complex variety, and has a mixed Hodge realization due to Richard Hain.
On the other hand, higher Chow groups were defined by Spencer Bloch as an example of a motivic cohomology. In this talk I will gently introduce the notion of archimedean height pairing, and then explore the possibility to generalize it to higher Chow cycles. This is a joint work in progress with Greg Pearlstein and José Ignacio Burgos Gil.