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arXiv · 1403.4412

Localization in equivariant operational K-theory and the Chang-Skjelbred property

Richard Gonzales
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Abstract

We establish a localization theorem of Borel-Atiyah-Segal type for the equivariant operational K-theory of Anderson and Payne. Inspired by the work of Chang-Skjelbred and Goresky-Kottwitz-MacPherson, we establish a general form of GKM theory in this setting, applicable to singular schemes with torus action. Our results are deduced from those in the smooth case via Gillet-Kimura's technique of cohomological descent for equivariant envelopes. As an application, we extend Uma's description of the equivariant K-theory of smooth compactifications of reductive groups to the equivariant operational K-theory of all, possibly singular, projective group embeddings.

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Richard Gonzales. 2014-03-18. Localization in equivariant operational K-theory and the Chang-Skjelbred property. https://arxiv.org/abs/1403.4412

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