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Title: Quantum multiplicative hypertoric varieties and localization
Author: Cooney, Nicholas
ISNI:       0000 0004 5915 6333
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2014
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In this thesis, we consider q-deformations of multiplicative Hypertoric varieties, where q∈𝕂x for 𝕂 an algebraically closed field of characteristic 0. We construct an algebra Dq of q-difference operators as a Heisenberg double in a braided monoidal category. We then focus on the case where q is specialized to a root of unity. In this setting, we use Dq to construct an Azumaya algebra on an l-twist of the multiplicative Hypertoric variety, before showing that this algebra splits over the fibers of both the moment and resolution maps. Finally, we sketch a derived localization theorem for these Azumaya algebras.
Supervisor: Kremnitzer, Yakov Sponsor: Engineering & Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Mathematics ; Algebraic geometry ; Group theory and generalizations (mathematics) ; Representation Theory ; Quantum Algebra ; Braided Tensor Categories ; Azumaya algebras