Skip to main content
Log in

Torsion Points of Generalized Honda Formal Groups

  • TO THE 75TH BIRTHDAY OF S.V. VOSTOKOV
  • Published:
Vestnik St. Petersburg University, Mathematics Aims and scope Submit manuscript

Abstract

Generalized Honda formal groups are a class of formal groups, which includes all formal groups over the ring of integers of local fields weakly ramified over \({{\mathbb{Q}}_{p}}\). This class is the next in the chain multiplicative formal group–Lubin-Tate formal groups–Honda formal groups. The Lubin-Tate formal groups are defined by distinguished endomorphisms [π]F. Honda formal groups have distinguished homomorphisms that factor through [π]F. In this article, we prove that for generalized Honda formal groups, the composition of a sequence of distinguished homomorphisms factors through [π]F . As an application of this fact, a number of properties of πn-torsion points of the generalized Honda formal group are proved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. T. Honda, “On the theory of commutative formal groups,” J. Math. Soc. Jpn. 22, 213–246 (1970).

    Article  MathSciNet  Google Scholar 

  2. D. G. Benois and S. V. Vostokov, “Norm pairing in formal groups and Galois representations,” Leningr. Math. J. 2, 1221–1249 (1991).

    MathSciNet  MATH  Google Scholar 

  3. O. V. Demchenko, “Honda formal groups: The arithmetic of the group of points,” St. Petersburg Math. J. 12, 101–115 (2001).

    MathSciNet  Google Scholar 

  4. O. V. Demchenko, “Formal groups over p-adic rings of integers with small ramification and distinguished isogenies,” St. Petersburg Math. J. 14, 405–428 (2003).

    MathSciNet  MATH  Google Scholar 

  5. O. Demchenko, “New relationship between formal Lubin-Tate groups and formal Honda groups,” St. Petersburg Math. J. 10, 785–789 (1999).

    MathSciNet  Google Scholar 

Download references

Funding

This study was supported by the Russian Science Foundation, project no. 16-11-10200.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to O. V. Demchenko or S. V. Vostokov.

Additional information

Translated by O. Pismenov

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Demchenko, O.V., Vostokov, S.V. Torsion Points of Generalized Honda Formal Groups. Vestnik St.Petersb. Univ.Math. 53, 404–411 (2020). https://doi.org/10.1134/S1063454120040044

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063454120040044

Keywords:

Navigation