Schema/Lokal freie Garben/Surjektiv/Kern/Fakt/en

Let ${}X$ denote a scheme and let ${}{\mathcal {F}}$ and ${}{\mathcal {G}}$ denote two locally free sheaves (of rank ${}r$ and ${}s$) together with a surjective sheaf homomorphism

$\psi \colon {\mathcal {F}}\longrightarrow {\mathcal {G}}.$

Then the kernel sheaf ${}\operatorname {kern} \psi$ is also locally free (of rank $r-s$).