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Mat. Sb., 2015, Volume 206, Number 9, Pages 21–98 (Mi msb8516)  

This article is cited in 12 scientific papers (total in 12 papers)

A higher-dimensional Contou-Carrère symbol: local theory

S. O. Gorchinskiy, D. V. Osipov

Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: We construct a higher-dimensional Contou-Carrère symbol and we study some of its fundamental properties. The higher-dimensional Contou-Carrère symbol is defined by means of the boundary map for $K$-groups. We prove its universal property. We provide an explicit formula for the higher-dimensional Contou-Carrère symbol over $\mathbb Q$ and we prove the integrality of this formula. We also study its relation with the higher-dimensional Witt pairing.
Bibliography: 46 titles.

Keywords: Contou-Carrère symbol, boundary map for $K$-groups, Witt pairing.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant no. 14-50-00005.


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English version:
Sbornik: Mathematics, 2015, 206:9, 1191–1259

Bibliographic databases:

ArXiv: 1505.03829
Document Type: Article
UDC: 512.71+512.666+511.687
MSC: Primary 19D45; Secondary 19F15
Received: 25.03.2015

Citation: S. O. Gorchinskiy, D. V. Osipov, “A higher-dimensional Contou-Carrère symbol: local theory”, Mat. Sb., 206:9 (2015), 21–98; Sb. Math., 206:9 (2015), 1191–1259

Citation in format AMSBIB
\by S.~O.~Gorchinskiy, D.~V.~Osipov
\paper A~higher-dimensional Contou-Carr\`ere symbol: local theory
\jour Mat. Sb.
\yr 2015
\vol 206
\issue 9
\pages 21--98
\jour Sb. Math.
\yr 2015
\vol 206
\issue 9
\pages 1191--1259

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    This publication is cited in the following articles:
    1. S. O. Gorchinskiy, D. V. Osipov, “Tangent space to Milnor $K$-groups of rings”, Proc. Steklov Inst. Math., 290:1 (2015), 26–34  mathnet  crossref  crossref  isi  elib  elib
    2. S. P. Suetin, “Distribution of the zeros of Padé polynomials and analytic continuation”, Russian Math. Surveys, 70:5 (2015), 901–951  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. 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
    4. 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
    5. V. V. Przyjalkowski, “Calabi-Yau compactifications of toric Landau-Ginzburg models for smooth Fano threefolds”, Sb. Math., 208:7 (2017), 992–1013  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. D. V. Osipov, “Second Chern numbers of vector bundles and higher adeles”, Bull. Korean Math. Soc., 54:5 (2017), 1699–1718  crossref  mathscinet  isi  scopus
    7. V. Przyjalkowski, C. Shramov, “Laurent phenomenon for Landau-Ginzburg models of complete intersections in Grassmannians of planes”, Bull. Korean Math. Soc., 54:5 (2017), 1527–1575  mathnet  crossref  mathscinet  isi  scopus
    8. V. V. Przyjalkowski, “On the Calabi–Yau Compactifications of Toric Landau–Ginzburg Models for Fano Complete Intersections”, Math. Notes, 103:1 (2018), 104–110  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. D. B. Kaledin, “Witt vectors, commutative and non-commutative”, Russian Math. Surveys, 73:1 (2018), 1–30  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    10. D. V. Osipov, “Adelic quotient group for algebraic surfaces”, St. Petersburg Math. J., 30 (2019), 111–122  mathnet  crossref  isi  elib
    11. 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
    12. 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
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