This article is cited in 8 papers

Tangent space to Milnor $K$-groups of rings

S. O. Gorchinskiy, D. V. Osipov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

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.

UDC: 512.666

Received: March 15, 2015

DOI: 10.1134/S0371968515030036

 English version: Proceedings of the Steklov Institute of Mathematics, 2015, 290:1, 26–34

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ArXiv: 1505.03780