Deformations of Bloch groups and Aomoto dilogarithms in characteristic p

In this paper, we study the Bloch group B₂(F₂[ε]) over the ring of dual numbers of the algebraic closure of the field with p elements, for a prime p?5. We show that a slight modification of Kontsevich?s -logarithm defines a function on B₂(F₂[ε]). Using this function and the characteristic p version of the additive dilogarithm function that we previously defined, we determine the structure of the infinitesimal part of B₂(F₂[ε]) completely. This enables us to define invariants on the group of deformations of Aomoto dilogarithms and determine its structure. This final result might be viewed as the analog of Hilbert?s third problem in characteristic p.