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.

💡 Research Summary

The paper investigates equivariant K‑theory for toric varieties and presents two principal results that together give a unified, algebraic description of the equivariant K‑groups in both affine and non‑affine settings.

The first part deals with an arbitrary affine toric variety X_σ defined by a rational convex cone σ ⊂ N_ℝ, where N is a lattice and M = Hom(N,ℤ) is its dual. The coordinate ring of X_σ is the monoid algebra k