of essentially finite vector bundles on $X$. See [@nori Definition, p.37-8].

Acknowledgements {#acknowledgements .unnumbered}
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The research of PHH is supported by the Vietnam National Foundation for Science and Technology Development (Nafosted) grant number 101.04-2016.19. Parts of his research on this work were carried out during several visits to France supported by the project “International Associated Laboratory FORMATH VIETNAM” of VAST, grant number QTFR01.04/18-19., the Institute Henri Poincaré, Paris, and a “Poste Rouge” grant from the CNRS, France. JPdS thanks A. Ducros for pointing out [@temkin10] and for useful discussions, Q. Liu for replying conscientiously to his e-mails concerning cohomological flatness, and I. Biswas as well as M. Romagny for answering some of his questions.

Subsidiary material {#subsidiary_material}
===================

We collect here some simple facts which are useful in developing our arguments.

\[03.07.2018–1\]Let $Y$ be a proper, reduced and connected scheme over the field $K$. If $Y$ has a $K$-point then $K=H^0({{\mathscr{O}}}_Y)$.

We know that $H^0({{\mathscr{O}}}_Y)=R_1{\times}\cdots{\times}R_m$, where each $R_i$ is a local Artin algebra. Since $Y$ is connected, we must have $m=1$. So $H^0({{\mathscr{O}}}_Y)$ is a local Artin algebra. Since $Y$ is reduced, $H^0({{\mathscr{O}}}_Y)$ is reduced, so $H^0({{\mathscr{O}}}_Y)$ is a finite field extension of $K$. The existence of a $K$-rational 