In this thesis, we consider q-deformations of multiplicative Hypertoric varieties, where q∈𝕂<sup>x</sup> for 𝕂 an algebraically closed field of characteristic 0. We construct an algebra D<sub>q</sub> 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 D<sub>q</sub> 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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:680407 |
| Date | January 2014 |
| Creators | Cooney, Nicholas |
| Contributors | Kremnitzer, Yakov |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://ora.ox.ac.uk/objects/uuid:17d0824f-e8f2-4cb7-9e84-dd3850a9e2a2 |
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