Higher algebraic K-theory for actions of diagonalizable groups
By G. Vezzosi, Angelo Vistoli. 2001
81 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f3cc310b8a8c83c4922f26957498a78b76bf7213
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Operational K-Theory (2013, unknown): “g of vector bundles K◦(X) is the quotient of K◦ T (X) by the ideal generated by differences of characters, giving a Ktheoretic analogue of the Stanley-Reisner presentation for the cohomology ring of X [VV]. These results may be seen as K-theory versions of GoreskyKottwitz-MacPherson (GKM) localizatio”
- Surjectivity for Hamiltonian G-spaces in K-theory (2005, methodology): “We give a topological proof based on that of [40], extending this result to actions of compact connected Lie groups, as well as to bundles possessing only a Spin c -structure instead of a complex structure.”