Ravenel's telescope conjecture for compactly generated triangulated categories

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Let D\mathcal{D} be a compactly generated triangulated category, and let t=(X,Y)\mathbf{t}=(\mathcal{X},\mathcal{Y}) be a smashing semiorthogonal decomposition of D\mathcal{D}.

Ravenel's telescope conjecture. The decomposition t\mathbf{t} is compactly generated.

This is the general triangulated-category formulation of Ravenel's telescope conjecture. The conjecture was refuted for the homotopy category of spectra, so the claim is not true in full generality.

References

Primary source

Lorenzo Martini, Carlos E. Parra, Manuel Saorín and Simone Virili, “Locally finitely presented Grothendieck categories with a flat generator”, arXiv:2508.00670 (2025).

Additional references

3 papers in this index state this conjecture (2019–2025). The statement above is taken from the most recent of them; the others are arXiv:1902.05046, arXiv:1901.09004.

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