Recollements for dualizing $k$-varieties and Auslander's formulas
Category Theory
2025-05-22 v1 Representation Theory
Abstract
Given the pair of a dualizing -variety and its functorially finite subcategory, we show that there exists a recollement consisting of their functor categories of finitely presented objects. We provide several applications for Auslander's formulas: The first one realizes a module category as a Serre quotient of a suitable functor category. The second one shows a close connection between Auslander-Bridger sequences and recollements. The third one gives a new proof of the higher defect formula which includes the higher Auslander-Reiten duality as a special case.
Keywords
Cite
@article{arxiv.1703.06224,
title = {Recollements for dualizing $k$-varieties and Auslander's formulas},
author = {Yasuaki Ogawa},
journal= {arXiv preprint arXiv:1703.06224},
year = {2025}
}