Tangent space to Milnor $K$-groups of rings

S. O. Gorchinskiy; D. V. Osipov

doi:10.1134/S0081543815060036

Tangent space to Milnor $K$-groups of rings

Algebraic Geometry 2015-09-29 v1 K-Theory and Homology

Authors: S. O. Gorchinskiy , D. V. Osipov

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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 K\"ahler 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.

Keywords

Milnor K-groups tangent space absolute Kähler differentials ring weakly 5-fold stable algebraic geometry

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@article{arxiv.1505.03780,
  title  = {Tangent space to Milnor $K$-groups of rings},
  author = {S. O. Gorchinskiy and D. V. Osipov},
  journal= {arXiv preprint arXiv:1505.03780},
  year   = {2015}
}

Comments

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

Tangent space to Milnor $K$-groups of rings

Abstract

Keywords

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