Fan cohomology and its application to equivariant K-theory of toric varieties

Suanne Au, University of Nebraska - Lincoln

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 Cech cohomology groups of the presheaf [Special characters omitted.] 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.

Recommended Citation

Suanne Au, "Fan cohomology and its application to equivariant K-theory of toric varieties" (January 1, 2009). ETD collection for University of Nebraska - Lincoln. Paper AAI3359857.
http://digitalcommons.unl.edu/dissertations/AAI3359857