Vector bundle on scheme/Torsor and H^1/Correspondence/Fact

Let ${}X$ denote a noetherian separated scheme and let

$p\colon V\longrightarrow X$

denote a geometric vector bundle on ${}X$ with sheaf of sections ${}{\mathcal {S}}$.

Then there exists a correspondence between first cohomology classes

${}c\in H^{1}(X,{\mathcal {S}})$

and geometric ${}V$-torsors.

Proof, Write another proof