Tangent space to Milnor K-groups of rings

Abstract

We prove that the tangent space to the ( n + 1)th Milnor K-group of a ring R is isomorphic to the group of n th absolute Kähler differentials of R when the ring R contains 1/2 and has sufficiently many invertible elements. More precisely, the latter condition means that R is weakly 5-fold stable in the sense of Morrow.