Coleman norm and trace operators for polynomial formal groups
https://doi.org/10.22405/2226-8383-2019-20-3-361-371
Abstract
In this paper are investigated a polynomial formal group analogues of the operators introduced by Coleman for the Lubin Tate formal group and the multiplicative formal group. Explicit constructions of the norm and trace operators for Laurent series are given, their main propirtes are checked. The eigenvalues and root values of these operators are also studied, and a homomorphism is constructed that connects the additive structure and the structure of the formal module on the set of formal power series.
About the Authors
Petr Nikolaevich PitalRussian Federation
Vladimir Mikhailovich Polyakov
Russian Federation
References
1. Lubin, J. One-parameter formal Lie groups over p-adic integer rings, Annals of Math. 80 (1964), 464–484.
2. Frohlich, A. Formal groups. Lecture Notes in Mathematics. Springer. 1968. Vol. 74.
3. Lubin, J. Entireness of the endomorphism rings of one-dimensional formal groups, Proc. American Math. Soc. 52, (1975), 8–9.
4. Vostokov, S. V., Volkov, V. V., Pak, G. K. “The Hilbert symbol of a polynomial formal group”, Problems in the theory of representations of algebras and groups. Part 23, Zap. Nauchn. Sem. POMI, 400, POMI, St. Petersburg, 2012, 127–132; J. Math. Sci. (N. Y.), 192:2 (2013), 196–199.
5. Lubin, Jonathan, and John Tate. “Formal Complex Multiplication in Local Fields.” Annals of Mathematics, vol. 81, no. 2, 1965, pp. 380–387.
6. Coleman, R. F., 1979, “Division values in local fields“, Invent. Math., vol. 53, no. 2, pp. 91–116.
7. Hazewinkel, Michiel. (1978). Formal Groups and Applications.
8. Coleman, Robert F. The dilogarithm and the norm residue symbol. Bulletin de la Société Math’ematique de France, Volume 109 (1981), pp. 373–402.
9. Coleman, Robert F. The arithmetic of Lubin-Tate division towers. Duke Math. J. 48 (1981), no. 2, 449–466.
Review
For citations:
Pital P.N., Polyakov V.M. Coleman norm and trace operators for polynomial formal groups. Chebyshevskii Sbornik. 2019;20(3):361-371. (In Russ.) https://doi.org/10.22405/2226-8383-2019-20-3-361-371
Views:
385
Email this article 