Consider $F$ an $O_X$-module is true in general that $Hom_{O_X}(O_X,F) \equiv F(X)$ ? Morover I need to prove that if $F$ is a flasque sheaf then $H^n(X,F)=0$ for $n>0$.
I think is beacuse the fact that the section functor $\Gamma(U,-)$ keeps an exact sequence of sheaves $$ 0 \to F \to I \to H \to 0 $$ to an exact sequence $$ 0 \to \Gamma(U,F) \to \Gamma(U,I) \to \Gamma(U,H) \to 0 $$ This implies that the derived functors $R\Gamma$ are all $0$ it is correct? Thanks for the help!!