Bloch group

Summary

The Bloch group $\mathcal{B}(F)$ of a field $F$ is an abelian group built from symbols $[x]$ for $x \in F \setminus \{0, 1\}$. The symbols satisfy the five-term relation of the dilogarithm. Suslin showed that it is closely related to the indecomposable part of $K_3(F)$. For number fields the Bloch–Wigner function on the Bloch group gives the Borel regulator on $K_3$. It therefore computes values of the Dedekind zeta function at $s = 2$.