Obstruction groups for extending deformations of subdiagrams to deformations of diagrams in the categories of ringed topoi and schemes

Beutel T. Obstruction groups for extending deformations of subdiagrams to deformations of diagrams in the categories of ringed topoi and schemes. Bielefeld: Universität Bielefeld; 2013.In this thesis we exhibit an obstruction group for the following deformation theoretic problem. Given a diagram and a subdiagram of ringed topoi over a fixed ringed topos $\mathcal{S}$ and given a deformation $\xi$ of the subdiagram, what is an obstruction group for finding a deformation of the diagram reducing to the given deformation $\xi$ of the subdiagram? We will calculate this obstruction group for a large variety of interesting cases as explicitly as possible. The results hold as well in the case of diagrams and subdiagrams of schemes over a fixed scheme $S$