Quantum multiplicative hypertoric varieties and localization - Cooney, N (2014)
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.