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 Trudy Mat. Inst. Steklova, 2016, Volume 294, Pages 54–75 (Mi tm3731)

This article is cited in 9 scientific papers (total in 9 papers)

Continuous homomorphisms between algebras of iterated Laurent series over a ring

Sergey O. Gorchinskiy, Denis V. Osipov

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: We study continuous homomorphisms between algebras of iterated Laurent series over a commutative ring. We give a full description of such homomorphisms in terms of discrete data determined by the images of parameters. In similar terms, we give a criterion of invertibility of an endomorphism and provide an explicit formula for the inverse endomorphism. We also study the behavior of the higher dimensional residue under continuous homomorphisms.

 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/S0371968516030031

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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 294, 47–66

Bibliographic databases:

ArXiv: 1604.07005
UDC: 512.71
Received: April 19, 2016

Citation: Sergey O. Gorchinskiy, Denis V. Osipov, “Continuous homomorphisms between algebras of iterated Laurent series over a ring”, Modern problems of mathematics, mechanics, and mathematical physics. II, Collected papers, Trudy Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016, 54–75; Proc. Steklov Inst. Math., 294 (2016), 47–66

Citation in format AMSBIB
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This publication is cited in the following articles:
1. S. O. Gorchinskiy, D. V. Osipov, “Higher-dimensional Contou-Carrère symbol and continuous automorphisms”, Funct. Anal. Appl., 50:4 (2016), 268–280
2. V. V. Przyjalkowski, “Calabi-Yau compactifications of toric Landau-Ginzburg models for smooth Fano threefolds”, Sb. Math., 208:7 (2017), 992–1013
3. 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
4. V. V. Przyjalkowski, “On the Calabi–Yau Compactifications of Toric Landau–Ginzburg Models for Fano Complete Intersections”, Math. Notes, 103:1 (2018), 104–110
5. S. O. Gorchinskiy, D. N. Tyurin, “Relative Milnor $K$-groups and differential forms of split nilpotent extensions”, Izv. Math., 82:5 (2018), 880–913
6. 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
7. D. V. Osipov, “Adelic quotient group for algebraic surfaces”, St. Petersburg Math. J., 30:1 (2019), 111–122
8. A. B. Zheglov, “Surprising examples of nonrational smooth spectral surfaces”, Sb. Math., 209:8 (2018), 1131–1154
9. S. O. Gorchinskiy, D. V. Osipov, “Iterated Laurent series over rings and the Contou-Carrère symbol”, Russian Math. Surveys, 75:6 (2020), 995–1066
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