We consider a finite rig-étale morphism f: Y → X of quasi-smooth Berkovich curves over a complete algebraically closed valued field extension k of ℚ_p and a skeleton Γ_f = (Γ_Y, Γ_X) of the morphism f. We prove that Γ_f radializes f if and only if Γ_X controls the pushforward of the constant p-adic differential equation \({f_*}\left( {{{\cal O}_Y},{d_Y}} \right)\).

Furthermore, when f is a finite morphism of open unit discs and k is of arbitrary characteristic, we prove that f is radial if and only if the number of preimages of a point x ∈ X, counted without multiplicity, only depends on the radius of the point x.

我们考虑一个有限钻机étale态射˚F：ÿ→X的在一个完整的代数闭的值字段扩展准平滑Berkovich压曲线ķ ℚ的_p和骨架Γ _˚F =（Γ _Ý，Γ _X态射的）˚F。我们证明Γ _˚F radializes ˚F当且仅当Γ _X控制不变的前推p进制微分方程\（{F _ *} \左（{{{\ CAL O校} _Y}，{d_Y}} \右） \）。

此外，当˚F是开放的单元盘的有限态射和ķ是任意的特性，我们证明˚F是径向当且仅当一个点的原像的数目X ∈ X，没有多重计数，只依赖于半径点x。