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Algebraic geometry
thesis
Solanki, Vinesh
2015-08-12T13:51:28.172000+00:00
Mathematical logic and foundations
ora:6492
Zilber, Boris
urn:uuid:3fa23b75-9b85-4dc2-9ad6-bdb20d61fe45
Zariski structures in noncommutative algebraic geometry and representation theory
2011
03C
born digital
18F
Quantum theory (mathematics)
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.
2012-10-04T13:05:02.704000+00:00
16G
81R
ora:6492
text
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