Higher algebraic K-theory for actions of diagonalizable groups
| Autor: | ANGELO VISTOLI, Gabriele Vezzosi |
|---|---|
| Přispěvatelé: | Vezzosi, G, Vistoli, Angelo |
| Rok vydání: | 2005 |
| Předmět: |
Discrete mathematics
Pure mathematics Ring theory Ring (mathematics) Mathematics::Commutative Algebra 14L30 General Mathematics 19E08 Toric variety K-Theory and Homology (math.KT) Algebraic cycle Mathematics - Algebraic Geometry Algebraic group Algebraic K-theory Mathematics - K-Theory and Homology Spectral sequence FOS: Mathematics Equivariant map Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Inventiones mathematicae. 161:219-224 |
| ISSN: | 1432-1297 0020-9910 |
| Popis: | 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. Comment: Addendum contains mainly a corrected definition of specialization maps, the previous one being wrong as noticed by A. Neeman. All the other results (in particular the main results) still hold. Several other typos also corrected |
| Databáze: | OpenAIRE |
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