Huneke’s Uniform Briançon–Skoda Conjecture

Establish that every excellent Noetherian reduced ring of finite Krull dimension satisfies the Uniform Briançon–Skoda Property: there exists an integer B ≥ 0 such that for all ideals I ⊆ R and all n ∈ N one has overline{I^{n+B}} ⊆ I^n.

Background

The paper recalls the Uniform Briançon–Skoda Property: a ring R satisfies it if there exists a constant B such that for all ideals I and all n, the integral closure overline{I^{n+B}} is contained in I^n. The authors attribute to Huneke the conjecture that every excellent Noetherian reduced ring of finite Krull dimension enjoys this uniform containment.

They cite results proving the property under additional assumptions (e.g., essentially of finite type over a local ring, F-finite in prime characteristic, or essentially of finite type over Z, together with excellence and reducedness). The full conjecture in complete generality remains open.