Quotient Morita Theory with Applications
Abstract
We study equivalences between quotient categories of module categories associated with Gabriel topologies. We establish necessary and sufficient conditions for a Morita context to induce an equivalence between quotient categories and characterize such equivalences in terms of Morita contexts after passing to rings of quotients. Motivated by Artin--Zhang's noncommutative Serre theorem, we introduce a notion of ampleness relative to a Gabriel topology and use it to characterize quotient categories of finitely generated modules under suitable noetherian hypotheses. As an application, we establish a sufficient condition under which the noncommutative Auslander theorem holds for actions of finite-dimensional Hopf algebras on AS-regular algebras without assuming that the Hopf algebras are semisimple.
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BibTeX
@misc{chen2026quotient,
title = {{Quotient Morita Theory with Applications}},
author = {Xuyang Chen and Haonan Li and Quanshui Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39160},
eprint = {2609.39160},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39160},
}
RIS
TY - UNPB
TI - Quotient Morita Theory with Applications
AU - Xuyang Chen
AU - Haonan Li
AU - Quanshui Wu
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39160
UR - https://arxiv.org/abs/2609.39160
AB - We study equivalences between quotient categories of module categories associated with Gabriel topologies. We establish necessary and sufficient conditions for a Morita context to induce an equivalence between quotient categories and characterize such equivalences in terms of Morita contexts after passing to rings of quotients. Motivated by Artin--Zhang's noncommutative Serre theorem, we introduce a notion of ampleness relative to a Gabriel topology and use it to characterize quotient categories of finitely generated modules under suitable noetherian hypotheses. As an application, we establish a sufficient condition under which the noncommutative Auslander theorem holds for actions of finite-dimensional Hopf algebras on AS-regular algebras without assuming that the Hopf algebras are semisimple.
ER -