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.