  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.
