X$ from a flat $A$-scheme. In the same vein, we offer Theorem \[MS\_theorem\] explaining how to trivialize any vector bundle ${{\mathscr{E}}}\in{\mathbf{VB}}(X)$ with essentially finite fibres by a finite morphism $Y\to X$ from a flat $A$-scheme. (It should be noted that the proof of this result is technically intricate, but the main idea comes straight from Theorem \[14.05.2018–1\].) The section then ends with a direct comparison between the category ${\mathfrak{T}}_X$ and the one studied by [@mehta-subramanian13], see Corollary \[23.11.2018–2\], where it is shown that vector bundles on ${\mathfrak{T}}_X$ agree with those introduced in op. cit.

Section \[14.01.2019–3\] gives further applications to the theory of torsors and shows that torsors under quasi-finite group schemes actually come from finite ones, see Theorem \[25.06.2018–1\]. Another salient point developed in this section is the comparison to the theory of [@antei-emsalem-gasbarri18]: By demonstrating that $\Pi(X,x_0)$ “classifies” pointed quasi-finite torsors over $X$ (Theorem \[13.03.2019–2\]) we prove that $\Pi(X,x_0)$ agrees with the group denoted $\pi_1(X,x_0)^{\rm qf}$ in op.cit., see Theorem \[13.03.2019–1\].

Notations and conventions {#notations_conventions .unnumbered}
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[On the base ring.]{} {#on-the-base-ring. .unnumbered}
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(1) We let $A$ be a discrete valuation ring with uniformizer $\pi$, field of fractions $K$ and residual field $k$. The quotient ring $A/(\pi^{n+1})$ 