TY - JOUR

T1 - Honda Formal Module in an Unramified p-Extension of a Local Field as a Galois Module

AU - Hakobyan, T. L.

AU - Vostokov, S. V.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - 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 OK relative to the extension K/K0 and a uniformizing element π ∈ K0 is given. This paper studies the structure of F(mM) 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 WF s is the πs-torsion and WF = ∪n=1 ∞WF n is the complete π-torsion of a fixed algebraic closure Kalg of the field K.

AB - 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 OK relative to the extension K/K0 and a uniformizing element π ∈ K0 is given. This paper studies the structure of F(mM) 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 WF s is the πs-torsion and WF = ∪n=1 ∞WF n is the complete π-torsion of a fixed algebraic closure Kalg of the field K.

KW - formal group

KW - Galois module

KW - local field

KW - unramified extension

UR - http://www.scopus.com/inward/record.url?scp=85061183909&partnerID=8YFLogxK

U2 - 10.3103/S1063454118040027

DO - 10.3103/S1063454118040027

M3 - Article

AN - SCOPUS:85061183909

VL - 51

SP - 317

EP - 321

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -