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Abstract

n this thesis we study Fourier-Mukai transforms between derived categories of twisted sheaves. We show that some well known results about the classification of surfaces under derived categories extend to the derived category of twisted sheaves. In particular, we study the relationship between the derived category of twisted sheaves D^b(X,\alpha) for an Enriques surface Y and the derived category of twisted sheaves $D^b(X,\pi^{\ast}\alpha)$ where $\pi^{\ast}:Br'(Y)\rightarrow Br'(X)$ is the induced homomorphism obtained from the K3 cover of Y: $\pi:X\rightarrow Y$. We also study the injectivity of the morphism $\pi^{\ast}:Br'(Y)\rightarrow Br'(X)$.