John Rognes: `On the image of Milnor's K4 in Quillen's K4'.

For a field F, there is a natural map from Milnor K-theory KM(F) to Quillen's algebraic K-theory K(F). The map is an isomorphism in dimensions <= 2, and its image is well understood in dimension 3. When F is a number field, the image is zero in dimensions >= 5. Addressing a question of Suslin, we give a lower bound on the order of the image in dimension 4, which is sometimes nontrivial for real number fields.