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Honda Formal Module in an Unramified p-Extension of a Local Field as a Galois Module

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Abstract

For a fixed rational prime number p, consider a chain of finite extensions of fields K0/ℚp, K/K0, L/K, and M/L, where K/K0 is an unramified extension and M/L is Galois extension with Galois group G. Suppose that a one-dimensional Honda formal group F over the ring \(\mathcal{O}_K\) relative to the extension K/K0 and a uniformizing element π ∈ K0 is given. This paper studies the structure of \(F(\mathfrak{m}_M)\) as an \(\mathcal{O}_{K_0}\)[G]-module for an unramified p-extension M/L provided that \(W_F\cap{F({\frak{m}}_L)}=W_F\cap{F({\frak{m}}_M)}=W_F^s\) for some s ≥ 1, where W s F is the πs-torsion and WF = ∪n=1∞WFn is the complete π-torsion of a fixed algebraic closure Kalg of the field K.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, 199034, Russia

    T. L. Hakobyan & S. V. Vostokov

Authors
  1. T. L. Hakobyan
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  2. S. V. Vostokov
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Correspondence to T. L. Hakobyan.

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Original Russian Text © T.L. Hakobyan, S.V. Vostokov, 2018, published in Vestnik Sankt-Peterburgskogo Universiteta: Matematika, Mekhanika, Astronomiya, 2018, Vol. 51, No. 4, pp. 541–548.

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Hakobyan, T.L., Vostokov, S.V. Honda Formal Module in an Unramified p-Extension of a Local Field as a Galois Module. Vestnik St.Petersb. Univ.Math. 51, 317–321 (2018). https://doi.org/10.3103/S1063454118040027

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  • DOI: https://doi.org/10.3103/S1063454118040027

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