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Higher algebraic K-theory for actions of diagonalizable groups

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An Erratum to this article was published on 07 April 2005

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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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Bologna, 40126, Bologna, Italy

    Gabriele Vezzosi & Angelo Vistoli

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  1. Gabriele Vezzosi
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  2. Angelo Vistoli
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Correspondence to Gabriele Vezzosi or Angelo Vistoli.

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Mathematics Subject Classification (2000)

19E08, 14L30

An erratum to this article is available at http://dx.doi.org/10.1007/s00222-005-0429-0.

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Vezzosi, G., Vistoli, A. Higher algebraic K-theory for actions of diagonalizable groups. Invent. math. 153, 1–44 (2003). https://doi.org/10.1007/s00222-002-0275-2

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