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Iterated extensions and relative Lubin-Tate groups

Abstract : Let K be a finite extension of Q_p with residue field F_q and let P(T) = T^d + a_{d-1}T^{d-1} + ... +a_1 T, where d is a power of q and a_i is in the maximal ideal of K for all i. Let u_0 be a uniformizer of O_K and let {u_n}_{n \geq 0} be a sequence of elements of Q_p^alg such that P(u_{n+1}) = u_n for all n \geq 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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https://hal.archives-ouvertes.fr/hal-01116294
Contributor : Laurent Berger Connect in order to contact the contributor
Submitted on : Friday, February 13, 2015 - 9:02:25 AM
Last modification on : Tuesday, November 19, 2019 - 12:49:50 PM

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  • HAL Id : hal-01116294, version 1
  • ARXIV : 1411.7064

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Laurent Berger. Iterated extensions and relative Lubin-Tate groups. Annales des sciences mathématiques du Québec, 2016. ⟨hal-01116294⟩

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