Zariski structures in noncommutative algebraic geometry and representation theory

Thesis

A suitable subcategory of affine Azumaya algebras is defined and a functor from this category to the category of Zariski structures is constructed. The rudiments of a theory of presheaves of topological structures is developed and applied to construct examples of structures at a generic parameter. The category of equivariant algebras is defined and a first-order theory is associated to each object. For those theories satisfying a certain technical condition, uncountable categoricity and quantifier elimination results are established. Models are shown to be Zariski structures and a functor from the category of equivariant algebras to Zariski structures is constructed. The two functors obtained in the thesis are shown to agree on a nontrivial class of algebras.

Authors: Solanki, V

• Publication date: 2011
• DOI: 10.5287/ora-konepprxv
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: Oxford University, UK
• Language: English
• Keywords: 18F; 81R; 03C; 16G
• Subjects: Mathematical logic and foundations; Quantum theory (mathematics); Algebraic geometry