Characteristic tilting modules and Ringel duality in the Noetherian world
Abstract
The foundations of Ringel duality for split quasi-hereditary algebras over commutative Noetherian rings are strengthened. Several descriptions and properties of the smallest resolving subcategory containing all standard modules over split quasi-hereditary algebras over commutative Noetherian rings are provided. In particular, given two split quasi-hereditary algebras and , we prove that any exact equivalence between the smallest resolving subcategory containing all standard modules over and the smallest resolving subcategory containing all standard modules over lifts to a Morita equivalence between and which preserves the quasi-hereditary structure.
Cite
@article{arxiv.2405.00729,
title = {Characteristic tilting modules and Ringel duality in the Noetherian world},
author = {Tiago Cruz},
journal= {arXiv preprint arXiv:2405.00729},
year = {2024}
}
Comments
The first part was previously the appendix of the paper arXiv:2208.00291 while the latter part contains parts removed of the second version of the paper arXiv:2210.09344. 26 pages