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arXiv · 2311.00601

Telescope conjecture via homological residue fields with applications to schemes

Michal Hrbek
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Abstract

For a big tt-category, we give a characterization of the Telescope Conjecture (TC) in terms of definable tensor-ideals generated by homological residue fields. We formulate a stalk-locality property of (TC) and prove that it holds in the case of the derived category of a quasi-compact quasi-separated scheme, strengthening a result \cite{HHZ21}. As an application, we find strong links between (TC) and separation properties of the adic topology on local rings. This allows us to recover known examples and counterexamples of when (TC) holds over a scheme, as well as to construct some new ones.

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Michal Hrbek. 2024-09-29. Telescope conjecture via homological residue fields with applications to schemes. https://doi.org/10.2140/tunis.2025.7.199

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