Английская Википедия:Goncharov conjecture
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In mathematics, the Goncharov conjecture is a conjecture introduced by Шаблон:Harvs suggesting that the cohomology of certain motivic complexes coincides with pieces of K-groups. It extends a conjecture due to Шаблон:Harvs.
Statement
Let F be a field. Goncharov defined the following complex called <math>\Gamma(F,n)</math> placed in degrees <math>[1,n]</math>:
- <math>\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. </math>
He conjectured that i-th cohomology of this complex is isomorphic to the motivic cohomology group <math>H^i_{mot}(F,\mathbb Q(n))</math>.
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