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On functional equations for Chow polylogarithms

open access: yes
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality ...
openaire   +2 more sources

The realization of the degree zero part of the motivic polylogarithm on abelian schemes in Deligne–Beilinson cohomology

open access: yes, 2017
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 ...
Scarponi, Danny, Danny Scarponi
core   +1 more source

Functional equations of polylogarithms in motivic cohomology

open access: yes, 2008
For an infinite field F, we study the integral relationship between the Bloch group B_2(F) and the higher Chow group CH^2(F,3) by proving some relations corresponding to the functional equations of the dilogarithm. As a second result, the groups involved in Suslin’s exact sequence 0 → Tor^1(F^× ,F^×)∼ → CH^2(F,3) → B_2(F) → 0 are identified with homology ...
openaire   +3 more sources

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