Use this URL to cite or link to this record in EThOS:
Title: Zariski structures in noncommutative algebraic geometry and representation theory
Author: Solanki, Vinesh
ISNI:       0000 0004 2733 8490
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2011
Availability of Full Text:
Access from EThOS:
Full text unavailable from EThOS. Please try the link below.
Access from Institution:
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.
Supervisor: Zilber, Boris Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Mathematical logic and foundations ; Algebraic geometry ; Quantum theory (mathematics)