Panagiotis Kostas: The derived category of coherent sheaves and Rouquier dimension of triangulated categories

Abstract: The purpose of this thesis is twofold. On one hand, we introduce the basic theory on the bounded derived category of coherent sheaves on a scheme X and prove a result of Beilinson on the structure of the derived category of \(\mathbb{P}^n\). On the other hand, we introduce the Rouquier dimension of a triangulated category and present a conjecture by Orlov, stating that, under some conditions, one can recover the dimension of a scheme by looking at its bounded derived category.