Classification of dominant resolving subcategories by moderate functions

Abstract

Let R be a commutative Noetherian ring. Denote by $\mathrm{mod}R$ the category of finitely generated R-modules. In this paper, we study dominant resolving subcategories of $\mathrm{mod}R$. We introduce a new $\mathbb{N}$-valued function on $\mathrm{Spec}R$ which we call a moderate function. Under an acceptable assumption, we construct explicit bijections between the set of dominant resolving subcategories of $\mathrm{mod}R$ and the set of moderate functions on $\mathrm{Spec}R$.