Iterated extensions and relative Lubin-Tate groups

2014/11/25 by Berger, Laurent · 1 citation
#11S05 #11S15 #11S20 #11S31 #11S82 #13F25 #14F30 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1411.7064

Abstract

Let K be a finite extension of Q_p with residue field F_q and let P(T) = T^d + a_d-1T^d-1 + ... +a₁ T, where d is a power of q and a_i is in the maximal ideal of K for all i. Let u₀ be a uniformizer of O_K and let u_{nn ≥ 0} be a sequence of elements of Q_p^alg such that P(u_n+1) = u_n for all n ≥ 0. Let K_infty be the field generated over K by all the u_n. If K_infty / K is a Galois extension, then it is abelian, and our main result is that it is generated by the torsion points of a relative Lubin-Tate group (a generalization of the usual Lubin-Tate groups). The proof of this involves generalizing the construction of Coleman power series, constructing some p-adic periods in Fontaine's rings, and using local class field theory.

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