## Abstract

For a fixed rational prime number p, consider a chain of finite extensions of fields K_{0}/ℚ_{p}, K/K_{0}, L/K, and M/L, where K/K_{0} 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 O_{K} relative to the extension K/K_{0} and a uniformizing element π ∈ K_{0} is given. This paper studies the structure of F(m_{M}) as an OK0[G]-module for an unramified p-extension M/L provided that WF∩F(mL)=WF∩F(mM)=WFs for some s ≥ 1, where W_{F} ^{s} is the π^{s}-torsion and W_{F} = ∪_{n=1} ^{∞}W_{F} ^{n} is the complete π-torsion of a fixed algebraic closure K^{alg} of the field K.

Original language | English |
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Pages (from-to) | 317-321 |

Number of pages | 5 |

Journal | Vestnik St. Petersburg University: Mathematics |

Volume | 51 |

Issue number | 4 |

DOIs | |

State | Published - 1 Oct 2018 |

## Scopus subject areas

- Mathematics(all)

## Keywords

- formal group
- Galois module
- local field
- unramified extension