Goncharov conjecture

In mathematics, the Goncharov conjecture is a conjecture introduced by suggesting that the cohomology of certain motivic complexes coincides with pieces of K-groups. It extends a conjecture due to.

Statement
Let F be a field. Goncharov defined the following complex called $$\Gamma(F,n)$$ placed in degrees $$[1,n]$$:
 * $$\Gamma_F(n)\colon \mathcal B_n(F)\to \mathcal B_{n-1}(F)\otimes F^\times_\mathbb Q\to\dots\to \Lambda^n F^\times_\mathbb Q. $$

He conjectured that i-th cohomology of this complex is isomorphic to the motivic cohomology group $$H^i_{mot}(F,\mathbb Q(n))$$.