Symmetric subcategories, tilting modules, and derived recollements

REVISTA MATEMATICA IBEROAMERICANA(2023)

Cited 0|Views0
No score
Abstract
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 symmet-ric subcategories associated to good 2-tilting modules over commutative Gorenstein local rings are presented.
More
Translated text
AI Read Science
Must-Reading Tree
Example
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined