Finitistic test ideals on numerically $\mathbb{Q}$-Gorenstein varieties

TL;DR

This paper proves that on numerically log e9tale e9quivalence classes of varieties, the finitistic and big test ideals coincide, advancing understanding of singularities in algebraic geometry.

Contribution

It establishes the equality of finitistic and big test ideals for numerically log e9tale e9quivalence classes, a significant step in singularity theory.

Findings

Finitistic and big test ideals coincide under certain conditions.

The result applies to numerically e9tale e9quivalence classes.

Advances the understanding of test ideals in algebraic geometry.

Abstract

We prove that the finitistic test ideal $\tau_{\rm fg}(R, \Delta, \mathfrak{a}^t)$ coincides with the big test ideal $\tau_{\rm b}(R, \Delta, \mathfrak{a}^t)$ if the pair $(R,\Delta)$ is numerically log $\mathbb{Q}$-Gorenstein.