Brandenburg, Martin: Tensor categorical foundations of algebraic geometry. 2014
Inhalt
- Introduction
- Preliminaries
- Introduction to cocomplete tensor categories
- Definitions and examples
- Categorification
- Element notation
- Adjunction between stacks and cocomplete tensor categories
- Commutative algebra in a cocomplete tensor category
- Algebras and modules
- Ideals and affine schemes
- Symtrivial objects
- Symmetric and exterior powers
- Derivations
- Flat objects
- Dualizable objects
- Invertible objects
- Locally free objects
- Descent theory
- Cohomology
- Constructions with cocomplete tensor categories
- Basic free constructions
- Global schemes and stacks
- Module categories over algebras
- Gradings
- Representations
- Local functors
- Tensoriality
- Localization
- Idempotents
- Projective tensor categories
- Definition and comparison to schemes
- Blow-ups
- The Segre embedding
- The Veronese embedding
- The Plücker embedding
- Products of schemes
- Tangent tensor categories
- Monoidal monads and their modules
- Bibliography