Characteristic tilting modules and Ringel duality in the Noetherian world

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.