Induction and restriction of (ϕ,Γ)-modules

2018/05/21 by de Shalit, Ehud, Porat, Gal
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1805.08103

Abstract

Let L be a non-archimedean local field of characteristic 0. We present a variant of the theory of (ϕ,Γ)-modules associated with Lubin-Tate groups, developed by Kisin and Ren [Ki-Re], in which we replace the Lubin-Tate tower by the maximal abelian extension Γ= Gal(L^ab/L). This variation allows us to compute the functors of induction and restriction for (ϕ,Γ)-modules, when the ground field L changes. We also give a self-contained account of the Cherbonnier-Colmez theorem on overconvergence in our setting.

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