Generation of D^b(C^*(BG)) by C^*(BT)

Establish that the bounded derived category D^b(C^*(BG)) is generated by the cochains module C^*(BT), where T is a maximal torus subgroup of the compact Lie group G.

Background

This conjecture (adapted from Benson and Greenlees’ Conjecture 1.7 for finite groups) proposes that the bounded derived category of cochains on BG is generated by the cochains on a maximal torus BT.

The paper proves that this conjecture is equivalent to the conjecture about generation by objects of the form Hom_{C_G}(k, X). It also shows the conjecture holds under the hypothesis that Db(C^(BG)) is generated by formal modules.

References

Conjecture [cf. 1.7] The bounded derived category $Db(C*(BG))$ is generated by the module $C*BT$, where $T$ is a maximal torus of $G$.

— The Nucleus of a Compact Lie Group, and Support of Singularity Categories (2405.00457 - Peirce, 1 May 2024) in Section 4.2, Conjectures on Generation