Lemma 94.14.9. Up to a replacement as in Stacks, Remark 8.4.9 the functor

$p : G\textit{-Torsors} \longrightarrow (\mathit{Sch}/S)_{fppf}$

defines a stack in groupoids over $(\mathit{Sch}/S)_{fppf}$.

Proof. The most difficult part of the proof is to show that we have descent for objects, which is Bootstrap, Lemma 79.11.8. We omit the proof of axioms (1) and (2) of Stacks, Definition 8.5.1. $\square$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).