Motivic interpretation of Milnor K-groups attached to Jacobian varieties, by Satoshi Mochizuki

In the paper, Somekawa, On Milnor K-groups attached at semi-abelian varieties, K-theory, vol. 4, 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 ismorphic to Ext^r_{M_k}(Z,G_1[-1] tensor ... tensor G_r[-1]) where 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 M_k as Voevodsky's category of motives DM^eff_-(k).

Satoshi Mochizuki <>