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Abstract
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For a big tt-category, we give a characterization of the telescope conjecture
in terms of
definable
-ideals
generated by homological residue fields. We formulate a stalk-locality property of
and prove that it holds in the case of the derived category of a
quasicompact quasiseparated scheme, strengthening the 2024 result from
Hrbek, Hu and Zhu. As an application, we find strong links between
and separation properties of the adic topology on local rings. This
allows us to recover known examples and counterexamples of when
holds
over a scheme, as well as to construct some new ones.
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Keywords
tensor triangulated category, telescope conjecture,
homological residue field, derived category, scheme
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Mathematical Subject Classification
Primary: 18G80, 18N55
Secondary: 13B35, 13H99
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Milestones
Received: 26 November 2023
Revised: 6 September 2024
Accepted: 28 September 2024
Published: 7 March 2025
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© 2025 The Author(s), under
exclusive license to MSP (Mathematical Sciences
Publishers). |
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