Higher algebraic K-theory for actions of diagonalizable groups, by Gabriele Vezzosi and Angelo Vistoli

We study the K-theory of actions of diagonalizable group schemes on regular algebraic spaces: our main result shows how to reconstruct the K-theory ring of such an action from the K-theory rings of the loci where the stabilizers have constant dimension. We apply this to the calculation of the equivariant K-theory of toric varieties, give conditions under which the Merkurjev spectral sequence degenerates, and prove a very refined localization theorem.

Gabriele Vezzosi <vezzosi@dm.unibo.it>
Angelo Vistoli <vistoli@dm.unibo.it>