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Higher algebraic K-theory for actions of diagonalizable groups

Gabriele Vezzosi·Angelo Vistoli
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Abstract

We study the K-theory of actions of diagonalizable group schemes on noetherian regular separated 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, and give conditions under which the Merkurjev spectral sequence degenerates, so that the equivariant K-theory ring determines the ordinary K-theory ring. We also prove a very refined localization theorem for actions of this type.

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Gabriele Vezzosi, Angelo Vistoli. 2004-09-17. Higher algebraic K-theory for actions of diagonalizable groups. https://arxiv.org/abs/math/0107174

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