Ideal sheaf of a closed subscheme (${\mathcal{I}}_{Z/X}$)

For a closed immersion $i:Z\hookrightarrow X$, the ideal sheaf is the kernel ${\mathcal{I}}_{Z/X}=\ker ({\mathcal{O}}_X\to i_{\ast }{\mathcal{O}}_Z)$. It therefore fits into the short exact sequence of sheaves