Compact sheaves on a locally compact space
Copyright policy )Compact sheaves on a locally compact space
Let X X be a hypercomplete locally compact Hausdorff space and let C \mathcal C be a compactly generated stable ∞ \infty -category. We describe the compact objects in the ∞ \infty -category of C \mathcal C -valued sheaves S h v ( X , C ) Shv(X,\mathcal C) . When X X is a non-compact connected manifold and C \mathcal C is the unbounded derived ∞ \infty -category of a ring, our result recovers a result of Neeman. Furthermore, if C \mathcal C is a nontrivial compactly generated stable ∞ \infty -category, we show that S h v ( X , C ) Shv(X,\mathcal C) is compactly generated if and only if X X is totally disconnected.
- University of Copenhagen Denmark
Mathematics - K-Theory and Homology, FOS: Mathematics, Algebraic Topology (math.AT), K-Theory and Homology (math.KT), Mathematics - Algebraic Topology
Mathematics - K-Theory and Homology, FOS: Mathematics, Algebraic Topology (math.AT), K-Theory and Homology (math.KT), Mathematics - Algebraic Topology
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