Equivariant vector bundles, their derived category and $K$-theory on affine schemes

Abstract

Let $G$ be an affine group scheme over a noetherian commutative ring $R$. We show that every $G$-equivariant vector bundle on an affine toric scheme over $R$ with $G$-action is extended from $\Spec(R)$ for several cases of $R$ and $G$. We show that given two affine schemes with group scheme actions, an equivalence of the equivariant derived categories implies isomorphism of the equivariant $K$-theories as well as equivariant $K^{\prime }$-theories.

arXiv comment34 pages, minor corrections, final version, to appear in Annals of K-Theory

Cited by in corpus (1)

• Toric Vector Bundles: GAGA and Hodge Theory