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.
|Titolo:||Higher algebraic K-theory for actions of diagonalizable groups|
|Data di pubblicazione:||2003|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/s00222-002-0275-2|
|Appare nelle tipologie:||1.1 Articolo in rivista|