In mathematics, the Goncharov conjecture is a conjecture introduced by Goncharov ( 1995) suggesting that the cohomology of certain motivic complexes coincides with pieces of K-groups. It extends a conjecture due to Zagier ( 1991).
Let F be a field. Goncharov defined the following complex called placed in degrees :
He conjectured that i-th cohomology of this complex is isomorphic to the motivic cohomology group .
In mathematics, the Goncharov conjecture is a conjecture introduced by Goncharov ( 1995) suggesting that the cohomology of certain motivic complexes coincides with pieces of K-groups. It extends a conjecture due to Zagier ( 1991).
Let F be a field. Goncharov defined the following complex called placed in degrees :
He conjectured that i-th cohomology of this complex is isomorphic to the motivic cohomology group .