Beutel, Tristan: Obstruction groups for extending deformations of subdiagrams to deformations of diagrams in the categories of ringed topoi and schemes. 2013
Inhalt
- Abstract
- Introduction
- Preliminaries
- The categories of topoi and ringed topoi
- Extensions of algebras
- The cotangent complex and its main properties
- Deformations of ringed topoi and schemes
- Diagrams of ringed topoi and schemes
- Deformations of diagrams and subdiagrams of ringed topoi
- The construction of a left adjoint to the forgetful functor
- The long exact sequence associated to the diagram and its subdiagram
- The simplification of the obstruction group
- Relations between a diagram, a subdiagram and a subsubdiagram
- Calculations of the obstruction group for particular cases
- Diagrams with at most three levels
- Deformations of diagrams of modules
- The relation between diagrams of modules and diagrams of ringed topoi
- The long exact sequence of a diagram and a subdiagram of modules
- The subdiagrams of a single morphism of modules
- Further properties of the cotangent complex
- Injective resolutions of modules on a diagram
- List of notations
- References
- Danksagung