Zilber, Boris
Solanki, Vinesh
Zariski structures in noncommutative algebraic geometry and representation theory
thesis
text
ora:6492
fedoraAdmin
2011
born digital
03C
Mathematical logic and foundations
18F
Algebraic geometry
81R
16G
Quantum theory (mathematics)
en
ora:6492
urn:uuid:3fa23b75-9b85-4dc2-9ad6-bdb20d61fe45
2012-10-04T13:05:02.704Z
2014-02-04T22:52:04.306Z
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.