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EnglishWe 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.
http://hdl.handle.net/11384/7410| Titolo: | Higher algebraic K-theory for actions of diagonalizable groups |
| Autori interni: | VISTOLI, ANGELO |
| Data di pubblicazione: | 2003 |
| Rivista: | INVENTIONES MATHEMATICAE |
| 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. |
| Handle: | http://hdl.handle.net/11384/7410 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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