The rational Whitehead injectivity conjecture

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For a group GG, let Wh⁡(G)\operatorname{Wh}(G) denote its Whitehead group, and let F ⁣in\mathcal{F}\!\mathit{in} be the family of finite subgroups. The rational Whitehead injectivity conjecture. The map

colim⁡H∈Ob⁡Sub⁡G(F ⁣in)Wh⁡(H)⊗ZQ⟶Wh⁡(G)⊗ZQ\operatorname*{colim}_{H\in\operatorname{Ob}\operatorname{Sub}_G(\mathcal{F}\!\mathit{in})}\operatorname{Wh}(H)\otimes_{\mathbb{Z}}\mathbb{Q}\longrightarrow\operatorname{Wh}(G)\otimes_{\mathbb{Z}}\mathbb{Q}

is injective. The source presents this as the torsion analogue of the torsion-free Whitehead conjecture and does not state a general resolution.

References

Primary source

Holger Reich and Marco Varisco, “Algebraic K-theory, assembly maps, controlled algebra, and trace methods”, arXiv:1702.02218 (2018).

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