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Vestnik St. Petersburg University, Mathematics

, Volume 51, Issue 4, pp 317–321 | Cite as

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

  • T. L. HakobyanEmail author
  • S. V. Vostokov
Mathematics
  • 3 Downloads

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 F s is the πs-torsion and WF = ∪n=1WFn is the complete π-torsion of a fixed algebraic closure Kalg of the field K.

Keywords

local field unramified extension formal group Galois module 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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