Zusammenfassung
In 2014, Kings and Rossler showed that the realization of the degree zero part of the abelian polylogarithm in analytic Deligne cohomology can be described in terms of a class of currents which was previously defined by Maillot and Rossler and strongly related to the Bismut-Kohler higher torsion form of the Poincare bundle. In this paper we show that, if the base of the abelian scheme is proper, ...
Zusammenfassung
In 2014, Kings and Rossler showed that the realization of the degree zero part of the abelian polylogarithm in analytic Deligne cohomology can be described in terms of a class of currents which was previously defined by Maillot and Rossler and strongly related to the Bismut-Kohler higher torsion form of the Poincare bundle. In this paper we show that, if the base of the abelian scheme is proper, Kings and Rossler's result can be refined to hold already in Deligne-Beilinson cohomology. More precisely, by means of Burgos' theory of arithmetic Chow groups, we prove that the class of currents defined by Maillot and Rossler has a representative with logarithmic singularities at the boundary and therefore defines an element in Deligne-Beilinson cohomology. This element coincides with the realization of the degree zero part of the motivic polylogarithm on abelian schemes in Deligne-Beilinson cohomology.
Altmetric