Honda formal group as Galois module in unramified extensions of local fields

2018/10/03 by Hakobyan, Tigran, Vostokov, Sergei
#11S20 #11S31 #14L05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1810.01695

Abstract

For given rational prime number p consider the tower of finite extensions of fields K₀/ℚ_p, K/K₀, L/K, M/L, where K/K₀ is unramified and M/L is a Galois extension with Galois group G. Suppose one dimensional Honda formal group over the ring O_K, relative to the extension K/K₀ and uniformizer π∈ K₀ is given. The operation x\undersetF+y=F(x,y) sets a new structure of abelian group on the maximal ideal \mathfrakp_M of the ring O_M which we will denote by F(\mathfrakp_M). In this paper the structure of F(\mathfrakp_M) as O_K0[G]-module is studied for specific unramified p-extensions M/L.

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