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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.


DOI: https://doi.org/10.4213/sm8516

Full text: PDF file (1076 kB)
References: PDF file   HTML file

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

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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, “Ob adelnoi faktorgruppe dlya algebraicheskoi poverkhnosti”, Algebra i analiz, 30:1 (2018), 151–169  mathnet  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
    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
  • Математический сборник Sbornik: Mathematics (from 1967)
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