The equivariant K-theory of toric varieties

TL;DR

This paper advances the understanding of equivariant K-theory for toric varieties by providing a general formula for affine cases and a new proof for smooth varieties, broadening theoretical insights in algebraic geometry.

Contribution

It introduces a generalized formula for equivariant K-groups of affine toric varieties and offers a novel proof for the K-theory of smooth toric varieties, extending existing results.

Findings

Derived a formula for equivariant K-groups of affine toric varieties.

Provided a new proof for the equivariant K-theory of smooth toric varieties.

Generalized known formulas to broader classes of toric varieties.

Abstract

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.