Compact sheaves on a locally compact space

2023/09/21 by Harr, Oscar
#Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2309.12127

Abstract

We describe the compact objects in the ∞-category of \mathcal C-valued sheaves Shv (X,\mathcal C) on a hypercomplete locally compact Hausdorff space X, for \mathcal C a compactly generated stable ∞-category. When X is a non-compact connected manifold and \mathcal C is the unbounded derived category of a ring, our result recovers a result of Neeman. Furthermore, for X as above and \mathcal C a nontrivial compactly generated stable ∞-category, we show that Shv (X,\mathcal C) is compactly generated if and only if X is totally disconnected.

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