Endlicher Körper/Projektive glatte Kurve/Vektorbündel/Stark semistabil Grad 0/Trivialisierbar/Fakt/en/Beweis
Erscheinungsbild
Beweis
We consider the family of locally free sheaves , . Because these are all semistable of degree , and defined over the same finite field, we must have (by the existence of the moduli space for vector bundles) a repetition, i.e.
for some . By Fakt the bundle admits an étale trivialization . Hence the finite map trivializes the bundle.