For H1F groups of type FP∞, the Balmer spectrum of dualisable objects is Proj(H*(G,k)) and the telescope conjecture holds, while infinite free products give Stone-Cech spectra and failures of the telescope conjecture and stratification.
Volume II, Hindustan Book Agency, New Delhi, 2010, pp
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The Balmer spectrum and telescope conjecture for infinite groups
For H1F groups of type FP∞, the Balmer spectrum of dualisable objects is Proj(H*(G,k)) and the telescope conjecture holds, while infinite free products give Stone-Cech spectra and failures of the telescope conjecture and stratification.