On $$\psi $$-Lattices in Modular $$(\varphi ,\Gamma )$$-Modules

Abstract

Let F/Q p be a finite field extension, let k be a finite field extension of the residue field of F . Generalizing the ψ-lattices which Colmez constructed in étale (ϕ, Γ)-modules over k[[t]][t −1 ], we define, study and exemplify ψ-lattices in étale (ϕ, Γ)-modules over k[[t 1 , . . . , t d ]][ i t −1 i ] for arbitrary d ∈ N.