Abstract
In 2014, Kings and Rössler 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 Rössler and strongly related to the Bismut–Köhler higher torsion form of the Poincaré bundle. In this paper we show that, if the base of the abelian scheme is proper, Kings and Rössler’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 Rössler 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.