we can construct the affine group scheme parametrising torsors, but we can naturally regard its category of representations in geometric terms. This facet is missing in [@antei-emsalem-gasbarri18] (since it is not understood what coherent modules are obtained by twisting representations via the fundamental torsor) as well as in [@mehta-subramanian13] (since the authors there focus solely on representations on free $A$-modules). On the downside, it is true that if no condition on the singularities of $X$ is imposed, then our approach ends up containing [*too much*]{} geometric information in the sense that it may account for torsors which are not necessarily finite over $X$; this is well understood in the case of non-normal schemes [@biswas-dos_santos12 Example 6]. Let us now review the remaining sections of the paper. Section \[subsidiary\_material\] serves to gather some simple facts from algebraic geometry (Lemmas \[03.07.2018–1\], \[03.07.2018–2\] and \[03.05.2018–1\]), to fix notation for a class of morphisms which is used allover in the paper (see Definition \[26.06.2018–1\]) and to put forward criteria allowing to decide when a morphism of group schemes is faithfully flat (Lemma \[29.11.2018–1\] and Lemma \[21.03.2019–1\]).

It is in Section \[14.04.2018–3\] where our theory starts to take form. In it, we introduce the central 