Higher Auslander correspondence for dualizing $R$-varieties

Abstract

Let $R$ be a commutative artinian ring. We extend higher Auslander correspondence from Artin $R$-algebras of finite representation type to dualizing $R$-varieties. More precisely, for a positive integer $d$, we show that a dualizing $R$-variety is $d$-abelian if and only if it is a $d$-Auslander dualizing $R$-variety if and only if it is equivalent to a $d$-cluster-tilting subcategory of the category of finitely presented modules over a dualizing $R$-variety.

18 pages. Note the change in the title and the change of terminology from 'homological d-cluster-tilting subcategory' to 'dZ-cluster-tilting subcategory'

References in corpus (2)

• Higher Nakayama algebras I: Construction
• Right $n$-angulated categories arising from covariantly finite subcategories

Cited by in corpus (8)

• Higher Nakayama algebras I: Construction
• An introduction to higher Auslander-Reiten theory
• The symplectic geometry of higher Auslander algebras: Symmetric products of disks
• Projectively generated $d$-abelian categories are $d$-cluster tilting
• Recollements for dualizing $k$-varieties and Auslander's formulas
• $d\mathbb{Z}$-cluster tilting subcategories of singularity categories
• $n\mathbb{Z}$-Gorenstein cluster tilting subcategories
• A functorial approach to $n$-abelian categories