I have read that for a locally free sheaf $F$ on a scheme $X$ one has a canonical trace map
$\underline{Hom}_{O_X}(F,F)\rightarrow O_X$
where on the left side I mean the inner hom.
Can someone explain how I get this map?
Thanks a lot!
I have read that for a locally free sheaf $F$ on a scheme $X$ one has a canonical trace map
$\underline{Hom}_{O_X}(F,F)\rightarrow O_X$
where on the left side I mean the inner hom.
Can someone explain how I get this map?
Thanks a lot!
There's a canonical section of Hom(F,F) given by the identity map locally. This corresponds to a morphism $O_X \to Hom(F,F) = F^* \otimes F$. Now dualize and use that $F^{**} = F$ since you assumed $F$ is locally free.