endowed with a finite morphism to $X$, see the [*proof*]{} of Lemma 3.1 in [@mehta-subramanian13]. In our opinion, [@mehta-subramanian13] only offers a sketch of how to implement this beautiful idea: in the proof of [@mehta-subramanian13 Lemma 3.1] the necessary “base-change” to an extension of $A$ is not mentioned, neither is [@deninger-werner05 Theorem 17]. In addition, as far as we can see, the proof of Theorem 4.1 in [@mehta-subramanian13]—which should extend Lemma 3.1 of op. cit.—offers solely a construction of a smooth curve inside a projective and smooth $A$-scheme. Given all these considerations, we set out to put the method of Deninger and Werner in a more robust form. In doing so we are able to circumvent Liu’s theorem on the existence of semi-stable models of relative curves (a crucial point in [@deninger-werner05] and hence in [@mehta-subramanian13 Lemma 3.1]) by means of the reduced fibre theorem (Theorem \[reduced\_fibre\_theorem\]). The advantage is that the latter result holds for more general schemes than just curves. This allows us to show Theorem \[14.05.2018–1\] saying that an $F$-trivial vector bundle $E$ (see the introduction of Section \[06.03.2019–1\] for the definition) on $X_0$ becomes relatively trivial (Definition \[20.02.2019–3\]) after pull back by a finite morphism $Y\to 