Bredon sheaf cohomology

Guido Arnone; Devarshi Mukherjee; Thomas Nikolaus

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arXiv · 2604.08066

Bredon sheaf cohomology

Guido Arnone·Devarshi Mukherjee·Thomas Nikolaus

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Abstract

For a finite group $G$, we compute the algebraic $K$-theory of the category of equivariant sheaves on a locally compact Hausdorff $G$-space, generalizing a result of Efimov, and determine the equivariant $E$-theory of the $C^*$-algebra of continuous functions. These invariants admit natural descriptions in terms of a new equivariant cohomology theory, which we call Bredon sheaf cohomology. This theory recovers classical Bredon cohomology for $G$-CW complexes and ordinary sheaf cohomology when $G$ is trivial. We establish its basic structural properties and prove a strong uniqueness theorem: any functor from the category of locally compact Hausdorff $G$-spaces to a dualizable stable category satisfying equivariant open descent and cofiltered compact codescent is equivalent to Bredon sheaf cohomology, generalizing a result of Clausen.

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BibTeX RIS

Guido Arnone, Devarshi Mukherjee, Thomas Nikolaus. 2026-04-09. Bredon sheaf cohomology. https://arxiv.org/abs/2604.08066

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