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Equivariant K-Theory

In: Handbook of K-Theory

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  • Alexander S. Merkurjev

    (University of California, Department of Mathematics)

Abstract

The equivariant K-theory was developed by R. Thomason in [21]. Let an algebraic group G act on a variety X over a field F. We consider G-modules, i.e., $$ \mathcal{O}_{X} $$ -modules over X that are equipped with an G-action compatible with one on X. As in the non-equivariant case there are two categories: the abelian category ℳ(G; X) of coherent G-modules and the full subcategory $$ \mathcal{P}(G;X) $$ consisting of locally free $$ \mathcal{O}_{X} $$ -modules. The groups K' n (G; X) and K n (G; X) are defined as the K-groups of these two categories respectively.

Suggested Citation

  • Alexander S. Merkurjev, 2005. "Equivariant K-Theory," Springer Books, in: Eric M. Friedlander & Daniel R. Grayson (ed.), Handbook of K-Theory, chapter 0, pages 925-954, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-27855-9_18
    DOI: 10.1007/978-3-540-27855-9_18
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