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Let $A$ be a discrete valuation ring and $X$ a projective flat $A$-scheme carrying an $A$-point $x_0$. In recent times, a certain number of mathematicians has proposed constructions of an affine and flat group scheme $\Pi(X,x_0)$ over $A$ with the distinctive property that morphisms to finite and flat group schemes $\Pi(X,x_0)\to G$ should canonically correspond to pointed $G$-torsors over $X$. See [@gasbarri03], [@antei-emsalem-gasbarri18] and [@mehta-subramanian13]. These theories are of course the analogues of Nori’s [@nori]—developed in the case of a base [*field*]{}—and as such, might be treated by similar mechanisms. Let us recall that Nori’s theory can be developed through

1.  a Tannakian category of semi-stable vector bundles on $X$ [@nori], through

2.  the construction of fibre products of torsors [@nori82 Chapter 2], or through

3.  a Tannakian category of vector bundles which are trivialized by proper and surjective morphisms [@biswas-dos_santos11].

The works [@gasbarri03] and [@antei-emsalem-gasbarri18] adopt point of view $({\bf F})$, whereas [@mehta-subramanian13] opts for a variant of ([**SS**]{}). In the present paper we focus on ([**T**]{}) to construct the affine and flat group scheme $\Pi(X,x_0)$. The advantage of this approach is that we can realise ${{\mathrm{Rep}}_{A}(\Pi(X,x_0))}$ as a [*full*]{} abelian subcategory of ${\mathbf{coh}}(X)$ so that, not only 