Recollements for dualizing $k$-varieties and Auslander's formulas

TL;DR

This paper constructs recollements for dualizing $k$-varieties and their subcategories, providing new insights into Auslander's formulas, module categories, and higher Auslander-Reiten duality.

Contribution

It introduces a recollement framework linking dualizing $k$-varieties with functor categories, and applies this to Auslander's formulas and higher dualities.

Findings

Realizes module categories as Serre quotients of functor categories

Connects Auslander-Bridger sequences with recollements

Provides a new proof of the higher defect formula

Abstract

Given the pair of a dualizing $k$-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.