In this thesis, we will check "Flat Cover Conjecture" in the category of quasi coherent sheaves over an arbitrary scheme X, ie Qco(X). At the beginning, this conjecture was considered in "Injective and flat covers and resolvents" in 1981. It was proved in the category of modules in 2001. Later on, this conjecture was raised in Qco(X). Since there are not enough projectives in the category of quasi coherent sheaves on a ringed space, and quasi coherent sheaves play the role of modules, this is important to check this conjecture in Qco(X). The proof of flat cover conjecture in Qco(X) has three steps. In the first step, we describe what is meant by a module over a ring representation of a quiver. Then we introduce a type of these modules called "Quasi Coherent R-Modules" and we will describe them. In the second step we prove that the category of quasi coherent sheaves is equivalent to the category of quasi coherent R-modules over the corresponding quiver. Based on this step, it is sufficient to check the existence of flat cover of a quasi coherent R-module. In the third step, we will check the existence of flat cover by means of a new discussion in category theory which is called "Model Category". In fact we will use "The Small Object Argument" to solve this conjecture. Finally after the proof of this conjecture, we will explain some of its applicatio especially we construct the flat resolution of a quasi coherent sheaf over a scheme X. Using this resolution enables us to construct a sort of cohomology.