Symmetric subcategories, tilting modules, and derived recollements
- Autores: Hongxing Chen, Changchang Xi
- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 5, 2023, págs. 1771-1812
- Idioma: inglés
- DOI: 10.4171/RMI/1410
- Enlaces
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Resumen
We introduce symmetric subcategories of abelian categories and show that the derived category of the endomorphism ring of any good tilting module over a ring is a recollement of the derived categories of the given ring and a symmetric subcategory of the module category of the endomorphism ring, in the sense of Beilinson–Bernstein–Deligne. Thus the kernel of the total left-derived tensor functor induced by a good tilting module is always triangle equivalent to the derived category of a symmetric subcategory of a module category. Explicit descriptions of symmetric subcategories associated to good 2-tilting modules over commutative Gorenstein local rings are presented.
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