Duke Mathematical Journal

Higher algebraic K-theory of group actions with finite stabilizers

Gabriele Vezzosi and Angelo Vistoli

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We prove a decomposition theorem for the equivariant $K$-theory of actions of affine group schemes $G$ of finite type over a field on regular separated Noetherian algebraic spaces, under the hypothesis that the actions have finite geometric stabilizers and satisfy a rationality condition together with a technical condition that holds, for example, for $G$ abelian or smooth. We reduce the problem to the case of a ${\rm GL}\sb n$-action and finally to a split torus action.

Article information

Duke Math. J., Volume 113, Number 1 (2002), 1-55.

First available in Project Euclid: 18 June 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 19E08: $K$-theory of schemes [See also 14C35]
Secondary: 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]


Vezzosi, Gabriele; Vistoli, Angelo. Higher algebraic K -theory of group actions with finite stabilizers. Duke Math. J. 113 (2002), no. 1, 1--55. doi:10.1215/S0012-7094-02-11311-8. https://projecteuclid.org/euclid.dmj/1087575224

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