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.
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
This publication is cited in the following 10 articles:
D. V. Osipov, “Formal Bott–Thurston Cocycle and Part of a Formal Riemann–Roch Theorem”, Proc. Steklov Inst. Math., 320 (2023), 226–257
S. O. Gorchinskiy, D. V. Osipov, “Iterated Laurent series over rings and the Contou-Carrère symbol”, Russian Math. Surveys, 75:6 (2020), 995–1066
V. V. Przyjalkowski, “On the Calabi–Yau Compactifications of Toric Landau–Ginzburg Models for Fano Complete Intersections”, Math. Notes, 103:1 (2018), 104–110
S. O. Gorchinskiy, D. N. Tyurin, “Relative Milnor K-groups and differential forms of split nilpotent extensions”, Izv. Math., 82:5 (2018), 880–913
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
D. V. Osipov, “Adelic quotient group for algebraic surfaces”, St. Petersburg Math. J., 30:1 (2019), 111–122
A. B. Zheglov, “Surprising examples of nonrational smooth spectral surfaces”, Sb. Math., 209:8 (2018), 1131–1154
V. V. Przyjalkowski, “Calabi-Yau compactifications of toric Landau-Ginzburg models for smooth Fano threefolds”, Sb. Math., 208:7 (2017), 992–1013
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
S. O. Gorchinskiy, D. V. Osipov, “Higher-dimensional Contou-Carrère symbol and continuous automorphisms”, Funct. Anal. Appl., 50:4 (2016), 268–280
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