Finite field/Smooth projective curve/Vector bundle/Strongly semistable degree 0/Trivializable/Fact

Let ${}K$ denote a finite field (or the algebraic closure of a finite field) and let ${}X$ be a smooth projective curve over ${}K$. Let ${}{\mathcal {S}}$ be a strongly semistable locally free sheaf over ${}X$ of degree ${}0$.

Then there exists a finite morphism

$\varphi \colon Y\longrightarrow X$

such that ${}\varphi ^{*}({\mathcal {S}})$ is trivial.

Proof, Write another proof