A note on b-divisors and filtrations on a local ring

TL;DR

This paper establishes a correspondence between filtrations and b-divisors in Noetherian local domains and applies it to prove a recent conjecture in the global setting.

Contribution

It introduces a new correspondence between filtrations and b-divisors and verifies a conjecture of Roé-Urbinati.

Findings

Established a correspondence between filtrations and b-divisors.

Proved a recent conjecture of Roé-Urbinati.

Applicable to a broad class of Noetherian local domains.

Abstract

In this note, we prove a correspondence between filtrations and b-divisors over a general class of Noetherian local domains. As an application in the global setting, we prove a recent conjecture of Ro\'e-Urbinati.