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Existence of compact objects in E outside the finite-induction-generated thick subcategory

Determine whether there exist compact objects in the equivariant E-theory ∞-category E that do not lie in the thick subcategory generated by the objects Ind_H^G(e(ℂ)) for all finite subgroups H ≤ G.

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Background

The authors identify a supply of compact objects in E arising from induction from finite subgroups H of G applied to e(ℂ), and they show E is compactly assembled. However, they also explain that E is not generated by these specific compact objects; if it were, problematic consequences for the Baum–Connes conjecture would follow.

The open problem asks whether there are compact objects in E beyond the thick subcategory generated by these induced units, which would illuminate the landscape of compact objects in E and their generation properties.

References

At the end of this introduction we list some open questions. 2) Does $E$ admit compact objects which are not in the thick subcategory generated by the objects $\Ind_{H}{G}(e(\C))$ for all finite subgroups $H$ of $G$.

— $E$-theory is compactly assembled (2402.18228 - Bunke et al., 28 Feb 2024) in Introduction (end)