Higher algebraic K-theory for actions of diagonalizable groups

Details Higher algebraic K-theory for actions of diagonalizable groups Higher algebraic K-theory for actions of diagonalizable groups

2001-07-24

arxiv.org/abs/math/0107174v6

Mathematics

Algebraic Geometry

Addendum contains mainly a corrected definition of specialization maps, the previous one being wrong as noticed by A. Neeman.

Scientific paper

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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