Telescope conjecture via homological residue fields with applications to schemes
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913729037205504 |
|---|---|
| author | Hrbek, Michal |
| author_facet | Hrbek, Michal |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00601 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Telescope conjecture via homological residue fields with applications to schemes Hrbek, Michal Category Theory Commutative Algebra Algebraic Geometry Primary: 18G80, 18N55, Secondary: 13H99, 13B35 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. |
| title | Telescope conjecture via homological residue fields with applications to schemes |
| topic | Category Theory Commutative Algebra Algebraic Geometry Primary: 18G80, 18N55, Secondary: 13H99, 13B35 |
| url | https://arxiv.org/abs/2311.00601 |