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 .
Let F be a field. Goncharov defined the following complex called
\Gamma(F,n)
[1,n]
\GammaF(n)\colonlBn(F)\tolBn-1(F) ⊗
| n | |
| F | |
| Q\to...\toΛ |
| x | |
| F | |
| Q. |
He conjectured that i-th cohomology of this complex is isomorphic to the motivic cohomology group
| i | |
| H | |
| mot |
(F,Q(n))