Higher Chow cycles on Abelian Surfaces

In this talk we discuss the construction of  new
indecomposable higher Chow cycles on a principally polarized  Abelian
surface over a non- Archimedean local field, which generalize a
construction due to Collino. The construction uses a generalization -
due to Birkenhake and Wilhelm - of some classical work of Humbert and
can be used to prove a  non-Archimedean analogue of the
Hodge-D-conjecture in the case when the Abelian surface has good and
ordinary reduction.