In the paper M. Somekawa, { \it{ On Milnor $K$-groups attached at semi-Abelian varieties}}, K-theory, \textbf{ 4} (1990) p.105, Somekawa conjectures that his Milnor K-group $K(k,G_1,...,G_r)$ attached to semi-abelian varieties $G_1$,...,$G_r$ over a field $k$ is isomorphic to ${ \rm Ext}_{ \mathcal{ M}_k}^r(\mathbb{ Z},G_1[-1] \otimes ... \otimes G_r[-1])$ where $\mathcal{ M}_k$ is a certain category of motives over $k$. The purpose of this note is to give remarks on this conjecture, when we take $\mathcal{ M}_k$ as Voevodsky's category of motives ${ \rm DM}^{ eff}_{ -}(k)$ .
Categories: math.KT math.AG