The paper constructs multivariable period rings for p-adic false Tate curve extensions and shows they bridge (φ,Γ)-modules and (φ,τ)-modules in both categorical and cohomological settings.
Berger -- Lifting the field of norms , Journal de l’École polytechnique — Mathématiques 1 (2014), p
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Multivariable period rings of $p$-adic false Tate curve extension
The paper constructs multivariable period rings for p-adic false Tate curve extensions and shows they bridge (φ,Γ)-modules and (φ,τ)-modules in both categorical and cohomological settings.