3 research outputs found
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 ÄŒech cohomology groups of the presheaf KqT on X endowed with a topology. Using these calculations and Walker\u27s 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
The equivariant K-theory of toric varieties
This paper contains two results concerning the equivariant K-theory of toric
varieties. The first is a formula for the equivariant K-groups of an arbitrary
affine toric variety, generalizing the known formula for smooth ones. In fact,
this result is established in a more general context, involving the K-theory of
graded projective modules. The second result is a new proof of a theorem due to
Vezzosi and Vistoli concerning the equivariant K-theory of smooth (not
necessarily affine) toric varieties.Comment: 12 page