Reconstruction of schemes via the tensor triangulated category of perfect complexes

This elaborate consists of a detailed presentation of the construction introduced for the first time by Paul Balmer and aimed to define a locally ringed space associated to a given tensor triangulated category, the so called spectrum of the category. The focus of this thesis is the case of the tensor triangulated category of perfect complexes on a noetherian scheme X, the full triangulated subcategory of the derived category of sheaves of modules consisting of complexes of sheaves locally quasi-isomorphic to complexes of locally free sheaves. This category inherits the structure of derived tensor product of complexes of sheaves of modules, becoming a tensor triangulated category. Its spectrum is a scheme isomorphic to X, providing a powerful reconstruction result.