Mathematics, Department of
Department of Mathematics: Dissertations, Theses, and Student Research
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First Advisor
Mark E. Walker
Date of this Version
7-2009
Document Type
Dissertation
Abstract
Mu-Wan Huang, Mark Walker and I established an explicit formula for the equivariant K-groups of affine toric varieties. We also recovered a result due to Vezzosi and Vistoli, which expresses the equivariant K-groups of a smooth toric variety in terms of the K-groups of its maximal open affine toric subvarieties. This dissertation investigates the situation when the toric variety X is neither affine nor smooth. In many cases, we compute the Čech cohomology groups of the presheaf KqT on X endowed with a topology. Using these calculations and Walker's Localization Theorem for equivariant K-theory, we give explicit formulas for the equivariant K-groups of toric varieties associated to all two dimensional fans and certain three dimensional fans.
Included in
Algebra Commons, Algebraic Geometry Commons, Geometry and Topology Commons, Science and Mathematics Education Commons
Comments
A dissertation Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfilment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics. Under the Supervision of Mark Walker.
Lincoln, Nebraska: August, 2009
Copyright (c) 2009 Suanne Au.