notion of modules which are [*relatively trivial*]{} (Definition \[20.02.2019–3\]) and the category of modules which are relatively trivialized by a proper and surjective morphism (Definition \[05.09.2018–3\]). The first useful properties of the category of such modules are also developed in Section \[14.04.2018–3\]: we show how to find more convenient trivializations (see Lemma \[20.02.2019–4\]) and how to make the first steps towards controlling kernels and cokernels of morphisms between relatively trivial modules (Proposition \[05.04.2018–3\]).

In Section \[04.07.2018–1\], the work initiated in Section \[14.04.2018–3\] is taken further ahead and we show that—under mild assumptions on the base scheme $X$—the category of modules which become relatively trivial after being pulled back along a suitable morphism ${\varphi}:Y\to X$, call it ${\mathfrak{T}}_{\varphi}$, is in fact abelian, see Theorem \[06.04.2018–1\]. In addition, concentrating on the objects in ${\mathfrak{T}}_{\varphi}$ which can be “dominated” by locally free ones and using the fibre at an $A$-point $x_0$ of $X$, we construct a neutral Tannakian category (terminology is that of [@duong-hai18 Definition 1.2.5]) over $A$. We consequently obtain an affine and flat group scheme $\Pi(X,{\varphi},x_0)$ whose category of representations is naturally a full subcategory of ${\mathbf{coh}}(X)$, see Definition \[14.01.2019–2\].

If $K$ stands for the field of fractions of $A$ and 