Necessary and sufficient conditions for complements to presilting objects in triangulated categories are established via co-t-structures, plus an equivalence characterizing silting-discrete algebras.
Operations on t-structures and perverse coherent sheaves
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abstract
The notions of consistent pairs and consistent chains of t-structures are introduced. A theorem that two consistent chains of t-structures generate a distributive lattice is proven. The technique developed is then applied to the pairs of chains obtained from the standard t-structure on the derived category of coherent sheaves and the dual t-structure by means of the shift functor. This yields a family of t-structures whose hearts are known as perverse coherent sheaves.
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2024 1verdicts
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Fishing for complements
Necessary and sufficient conditions for complements to presilting objects in triangulated categories are established via co-t-structures, plus an equivalence characterizing silting-discrete algebras.