Maps on divisor class groups induced by ring homomorphisms of finite flat dimension

Abstract

Let ϕ : A → B be a ring homomorphism between Noetherian normal integral domains. We estab- lish a general criterion for ϕ to induce a homomorphism Cl(ϕ ):C l(A) → Cl(B) on divisor class groups. For instance, this criterion applies whenever ϕ has finite flat dimension; this special case generalizes the more classical situations where ϕ is flat or is surjective with kernel generated by an A-regular element. We extend some of Spiroff's work on the kernels of induced maps to this more general setting.