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2014 | OriginalPaper | Chapter

5. On Norm Maps and “Universal Norms” of Formal Groups Over Integer Rings of Local Fields

Author : Nikolaj M. Glazunov

Published in: Continuous and Distributed Systems

Publisher: Springer International Publishing

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Abstract

We review and investigate norm maps and “universal norms” of formal groups over integer ring of local and quasi-local fields. Theorem on triviality of universal norm group of one dimensional fornal groups of reduction height 3 over integer ring of local and quasi-local fields is presented. The theorem on triviality of universal norm group is based on the lemma about function that gives the minimal degree of elements of the subgroup \(F_{K}^{t}\) of the group \(F{_K}\) that contains the norm group \(N_{L/K} (F^{n}_L)\). In the case of formal groups of elliptic curves the function has used by O. N. Vvedenskii and is denoted as \(\mu (n)\). The proof of the lemma is also presented.

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Shafarevich, I.R.: Principal homogenious spaces over function fields (in Russian). Tr. Math. Steklov Inst. 64, 316–346 (1961)MATH

Tate, J.: Principal homogenious spaces for abelian varieties. J. Reine Angew. Math. 209, 98–99 (1962)

Ogg, A.: Cohomology of abelian varieties over function fields. Ann. Math. 76, 185–220 (1962)MathSciNetCrossRefMATH

Vvedenskii, O.N.: On local “class fields” of elliptic curves (in Russian). Izv. Akad. Nauk SSSR Math. USSR Izvestija Ser Mat. 37(1), 20–88 (1973)MathSciNet

Vvedenskii, O.N.: On quasi-local “class fields” of elliptic curves I (in Russian). Izv. Akad. Nauk SSSR Math. USSR Izvestija Ser Mat. 40(5), 969–992 (1976)MathSciNet

Vvedenskii, O.N.: Duality in elliptic curves over local fields I (in Russian). Izv. Akad. Nauk SSSR Math. USSR Izvestija Ser Mat. Tom 28(4), 1091–1112 (1964)MathSciNet

Vvedenskii, O.N.: Duality in elliptic curves over local fields II (in Russian). Izv. Akad. Nauk SSSR Math. USSR Izvestija Ser Mat. Tom 30(4), 891–922 (1966)MathSciNet

Glazunov, N.M.: On the “norm subgroups” of one-parameter formal groups over integer ring of local field (in Russian). Dokl. Akad. Nauk Ukr. SSR, Ser. A 11, 965–968 (1973)MathSciNet

Lubin, J.: One parameter formal Lie groups over \(\rho \)-adic integer rings. Ann. Math. 80(3), 464–484 (1964)MathSciNetCrossRefMATH

10.

Glazunov, N.M.: Remarks on \(n\)-dimensional commutative formal groups over integer ring of \(\rho \)-adic field (in Russian). Ukr. Math. J. 25(3), 352–355 (1973)MathSciNetMATH

11.

Hazewinkel, M.: Formal Groups. Academic Press, New York (1977)

12.

Cassels, J., Fröhlich, A. (eds.): Algebraic Number Theory. Academic Press, London (2003)

13.

Vvedenskii, O.N.: On “universal norms” of formal groups over integer ring of local fields (In Russian). Izv. Akad. Nauk SSSR Math. USSR Izvestija Ser Mat. Tom 37, 737–751 (1973)MathSciNet

14.

Glazunov, N.M.: Quasi-local class fields of elliptic curves and formal groups I. Proc. IAMM NANU 24, 87–98 (2012)

15.

Serre, J.-P. Géométrie algébrique. In: Proceedings of the International Congress of Mathematicians, pp.190–196. Institut Mittag-Leffler, Djursholm (1963)

Title: On Norm Maps and “Universal Norms” of Formal Groups Over Integer Rings of Local Fields
Author: Nikolaj M. Glazunov
Publisher: Springer International Publishing
Book: Continuous and Distributed Systems
Print ISBN: 978-3-319-03145-3

Electronic ISBN: 978-3-319-03146-0

Copyright Year: 2014
DOI: https://doi.org/10.1007/978-3-319-03146-0_5