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arXiv · 2405.00729

Characteristic tilting modules and Ringel duality in the Noetherian world

Tiago Cruz
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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 $A$ and $B$, we prove that any exact equivalence between the smallest resolving subcategory containing all standard modules over $A$ and the smallest resolving subcategory containing all standard modules over $B$ lifts to a Morita equivalence between $A$ and $B$ which preserves the quasi-hereditary structure.

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Tiago Cruz. 2024-04-27. Characteristic tilting modules and Ringel duality in the Noetherian world. https://arxiv.org/abs/2405.00729

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