ORA Thesis: "Zariski structures in noncommutative algebraic geometry and representation theory" - uuid:3fa23b75-9b85-4dc2-9ad6-bdb20d61fe45

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Thesis

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http://ora.ox.ac.uk/objects/ora:6492

Reference: Vinesh Solanki, (2011). Zariski structures in noncommutative algebraic geometry and representation theory. DPhil. University of Oxford.

Citable link to this page: http://ora.ox.ac.uk/objects/uuid:3fa23b75-9b85-4dc2-9ad6-bdb20d61fe45
 
Title: Zariski structures in noncommutative algebraic geometry and representation theory

Abstract: 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.


Digital Origin:Born digital
Type of Award:DPhil
Level of Award:Doctoral
Awarding Institution: University of Oxford
About The Authors
institutionUniversity of Oxford
facultyMathematical,Physical & Life Sciences Division - Mathematical Institute
researchGroupModel Theory
oxfordCollegeExeter College
fundingEPSRC
 
Contributors
Prof Boris Zilber More by this contributor
RoleSupervisor
 
Bibliographic Details
Issue Date: 2011
Copyright Date: 2011
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Urn: uuid:3fa23b75-9b85-4dc2-9ad6-bdb20d61fe45
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Member of collection : ora:thesis
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Copyright Holder: Vinesh Solanki
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