Silting subcategories restrict t-structures exactly when contravariantly finite in completions, yielding a categorical characterization of right coherent rings and extending Koenig-Yang correspondences to metric triangulated categories.
Neeman, The categories T c and T b c determine each other, preprint (2018), arXiv:1806.06471
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Proves that recollements of weakly approximable triangulated categories induce short exact sequences on triangulated subcategories and associated big singularity categories under mild assumptions, with applications to derived categories of rings, DG algebras, and schemes.
A survey of Rickard's derived Morita theory, its influence on compactly generated triangulated categories, and its role in Broué's abelian defect group conjecture, including an alternative proof approach via completion.
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Metrics on triangulated categories and restrictions of (co)-$t$-structures
Silting subcategories restrict t-structures exactly when contravariantly finite in completions, yielding a categorical characterization of right coherent rings and extending Koenig-Yang correspondences to metric triangulated categories.
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Localization theorems for weakly approximable triangulated categories
Proves that recollements of weakly approximable triangulated categories induce short exact sequences on triangulated subcategories and associated big singularity categories under mild assumptions, with applications to derived categories of rings, DG algebras, and schemes.
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Rickard's Derived Morita Theory: Review and Outlook
A survey of Rickard's derived Morita theory, its influence on compactly generated triangulated categories, and its role in Broué's abelian defect group conjecture, including an alternative proof approach via completion.