Endlicher Körper/Projektive glatte Kurve/Vektorbündel/Stark semistabil Grad nichtnegativ/Endliche Annulation/Fakt/en

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 ${}E$ be a strongly semistable locally free sheaf over ${}X$ of nonnegative degree and let ${}c\in H^{1}(X,E)$ denote a cohomology class.

Then there exists a finite morphism

$\varphi \colon Y\longrightarrow X$

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