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Fan cohomology and its application to equivariant K-theory of toric varieties
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 KTq 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.^
Au, Suanne, "Fan cohomology and its application to equivariant K-theory of toric varieties" (2009). ETD collection for University of Nebraska - Lincoln. AAI3359857.