Homomorphisms of generalized Honda formal groups
https://doi.org/10.22405/2226-8383-2025-26-4-98-107
Abstract
Generalized Honda formal groups are the next step in a chain of generalizations the multiplicative formal group – Lubin-Tate formal groups — relative Lubin-Tate formal groups — Honda formal groups. This paper continues the study of properties of this class of formal groups focusing on their homomorphisms. In particular, we show that every homomorphism of generalized Honda formal groups can be expressed as a composition of a chain of distinguished isogenies and an isomorphism. It implies that for any generalized Honda formal group of finite height an isogeny class contains only a finite number of isomorphism classes. The results obtained give an idea of the structure of homomorphisms of formal groups over an arbitrary 𝑝-adic ring
of integers.
About the Author
Oleg Vyacheslavovich Demchenko
Saint Petersburg State University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
References
1. Honda, T. 1970, “On the theory of commutative formal groups”, J. Math. Soc. Japan, vol.22, pp. 213–246.
2. Demchenko, O., Vostokov, S. 2020, “Torsion points of generalized Honda formal groups”, Vestnik St. Petersburg Univ. Math., vol.53, no.4, 404–411.
3. Demchenko, O. 2003, “Formal groups over 𝑝-adic rings of integers with small ramification, and distinguished isogenies”, St.Petersburg Math. J., vol.14, no.3, 405–428.
4. Demchenko, O. 1999, “New relationship between formal Lubin-Tate groups and formal Honda groups”, St.Petersburg Math. J., vol.10, no.5, 785–789.
5. de Shalit, E. 1985, “Relative Lubin–Tate groups”, Proc. Amer. Math. Soc., vol.95, pp. 1–4.
6. Lubin, J., Tate, J. 1965, “Formal complex multiplication in local fields”, Ann. of Math., vol.81, pp.380–387.
7. Bondarko, M., Vostokov, S. 2003, “Explicit classification of formal groups over local fields”, Proc. Steklov Math. Inst., vol.241, pp. 35–57.
8. Lubin, J. 1975,“Entireness of the endomorphism rings of one-dimensional formal groups”, Proc. Amer. Math. Soc., vol.52, pp.8–10.
Review
For citations:
Demchenko O.V. Homomorphisms of generalized Honda formal groups. Chebyshevskii Sbornik. 2025;26(4):98-107. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-4-98-107
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