Does upper shriek pullback in the category of coherent sheaves coincide with when we take it in the category of sheaves of abelian groups?
Let $f:Z\hookrightarrow X$ be a closed immersion, let $f_{gp}^!$ be the right adjoint of $f_*$ on the derived category of sheaves of abelian groups. Denote by $f_{coh}^!$ the similar adjoint but in the category of derived category of coherent sheaves. For $E$ a complex of coherent sheaves on $X$ does $f_{gp}^!E$ coincide with $f^!_{coh}E$?