If $X$ is a scheme and $Z$ is the closed subvariety, how to compute support of $O_Z$ on $X$? I think it is just $Z$, but now I am not sure!
Example: $X = Spec(R)$, $I \subset R$, $Z = Spec(R/I)$. Then $Ann_R(R/I) = I$ I think, so $Supp(i_*O_Z) = V(I) = Z$. Am I'm wrong?
I read that we can not always find the coherent sheaf $F$ on $Z$ such that $Supp(F) = Z$. That's why I'm confused.