Lifting of recollements and gluing of partial silting sets
| Autor: | Alexandra Zvonareva, Manuel Saorín |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Noetherian
Pure mathematics General Mathematics 01 natural sciences Lift (mathematics) Mathematics::K-Theory and Homology Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Category Theory (math.CT) 16E35 18E30 Representation Theory (math.RT) 0101 mathematics Mathematics::Representation Theory Equivalence (measure theory) Mathematics Mathematics::Rings and Algebras 010102 general mathematics Coproduct Mathematics - Category Theory Mathematics - Rings and Algebras Rings and Algebras (math.RA) Bounded function Torsion (algebra) 010307 mathematical physics Mathematics - Representation Theory |
| Zdroj: | Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 152:209-257 |
| ISSN: | 1473-7124 0308-2105 |
| Popis: | This paper focuses on recollements and silting theory in triangulated categories. It consists of two main parts. In the first part a criterion for a recollement of triangulated subcategories to lift to a torsion torsion-free triple (TTF triple) of ambient triangulated categories with coproducts is proved. As a consequence, lifting of TTF triples is possible for recollements of stable categories of repetitive algebras or self-injective finite length algebras and recollements of bounded derived categories of separated Noetherian schemes. When, in addition, the outer subcategories in the recollement are derived categories of small linear categories the conditions from the criterion are sufficient to lift the recollement to a recollement of ambient triangulated categories up to equivalence. In the second part we use these results to study the problem of constructing silting sets in the central category of a recollement generating the t-structure glued from the silting t-structures in the outer categories. In the case of a recollement of bounded derived categories of Artin algebras we provide an explicit construction for gluing classical silting objects. |
| Databáze: | OpenAIRE |
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