In 1955 Chevalley gave a uniform proof the the <a href="https://en.wikipedia.org/wiki/Chevalley%E2%80%93Shephard%E2%80%93Todd_theorem">Chevalley-Shephard-Todd theorem</a> which says that for a finite group $G$ acting on a complex vector space $V$, the following are equivalent:

(i) The algebra $S(V)^G$ of invariant polynomial functions on $V$ is a polynomial ring;

(ii) $G$ is generated by pseudoreflections.

I believe Serre observed that Chevalley's proof of (i) $\Rightarrow$ (ii) goes through verbatim in the case of a field of arbitrary characteristic (although (ii) $\Rightarrow$ (i) may fail).

EDIT: Whoops, according to comments at a previous MO question (https://mathoverflow.net/questions/32450/chevalley-shephard-todd-theorem), I might be conflating two things here- the issue of the characteristic of the field, and the issue of reflections versus pseudoreflections. I think what Serre actually observed regarding Chevalley's proof is that the implication (ii) $\Rightarrow$ (i) is true for pseuoreflections, whereas Chevalley had only stated it for reflections.

A scan of the relevant paper "Groupes finis d’automorphismes d’anneaux locaux réguliers" of Serre (in French) is here: https://www.math.purdue.edu/~wilker/misc/serre-enjf.pdf.