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 group of $n$-th absolute Kähler differentials of $R$ when the ring $R$ contains $\frac{1}{2}$ and has sufficiently many invertible elements. More precisely, the latter condition is that $R$ is weakly $5$-fold stable in the sense of Morrow.

11 pages, to appear in Proc. Steklov Inst. Math. vol. 290 (2015)

References in corpus (2)

• A higher-dimensional Contou-Carrère symbol: local theory
• A Goodwillie-type Theorem for Milnor K-Theory

Cited by in corpus (3)

• A higher-dimensional Contou-Carrère symbol: local theory
• Relative Milnor $K$-groups and differential forms of split nilpotent extensions
• Volume and symplectic structure for l-adic local systems