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Tr. Mat. Inst. Steklova, 2015, Volume 290, Pages 34–42 (Mi tm3638)  

This article is cited in 5 scientific papers (total in 5 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.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968515030036

Full text: PDF file (191 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 290:1, 26–34

Bibliographic databases:

ArXiv: 1505.03780
Document Type: Article
UDC: 512.666
Received: March 15, 2015

Citation: S. O. Gorchinskiy, D. V. Osipov, “Tangent space to Milnor $K$-groups of rings”, Modern problems of mathematics, mechanics, and mathematical physics, Collected papers, Tr. Mat. Inst. Steklova, 290, MAIK Nauka/Interperiodica, Moscow, 2015, 34–42; Proc. Steklov Inst. Math., 290:1 (2015), 26–34

Citation in format AMSBIB
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\paper Tangent space to Milnor $K$-groups of rings
\inbook Modern problems of mathematics, mechanics, and mathematical physics
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2015
\vol 290
\pages 34--42
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\pages 26--34
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    This publication is cited in the following articles:
    1. S. O. Gorchinskiy, D. V. Osipov, “A higher-dimensional Contou-Carrère symbol: local theory”, Sb. Math., 206:9 (2015), 1191–1259  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Sergey O. Gorchinskiy, Denis V. Osipov, “Continuous homomorphisms between algebras of iterated Laurent series over a ring”, Proc. Steklov Inst. Math., 294 (2016), 47–66  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. S. O. Gorchinskiy, D. V. Osipov, “Higher-dimensional Contou-Carrère symbol and continuous automorphisms”, Funct. Anal. Appl., 50:4 (2016), 268–280  mathnet  crossref  crossref  mathscinet  isi  elib
    4. S. O. Gorchinskiy, D. N. Tyurin, “Relative Milnor $K$-groups and differential forms of split nilpotent extensions”, Izv. Math., 82:5 (2018), 880–913  mathnet  crossref  crossref  adsnasa  isi  elib
    5. S. O. Gorchinskiy, D. M. Krekov, “An explicit formula for the norm in the theory of fields of norms”, Russian Math. Surveys, 73:2 (2018), 369–371  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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