I have some questions about flat families of sheaves. Would someone mind telling me about the following questions ? Let $S$ be a scheme over algebraically closed field $k$, $X$ be a projective scheme over $k$, and $E,F$ be quasi-coherent sheaves of finite presentation on $X \times_k S$. **Question1**:$E,F$ coherent ? **Question2**: In addition, if $E$ is a flat family of torsion free coherent sheaves on $X$(i.e.E is flat over $S$ and $E_t$ is torsion free coherent on $X (\forall t \in S$ : closed point)) ,$F$ is also a flat family of torsion free coherent sheaves on $X$, and $Hom(E_t,F_t)= 0(\forall t \in S$ : closed point),then $Hom(E,F)=0$ ?