The lower semicontinuity of the Frobenius splitting numbers

TL;DR

This paper proves that, under certain mild conditions, the normalized Frobenius splitting numbers of a local ring in prime characteristic vary in a lower semicontinuous manner, contributing to the understanding of their stability.

Contribution

It establishes the lower semicontinuity of Frobenius splitting numbers under mild conditions, a new property in the study of rings in prime characteristic.

Findings

Frobenius splitting numbers are lower semicontinuous

The result applies under mild conditions

Enhances understanding of Frobenius splitting behavior

Abstract

We show that, under mild conditions, the (normalized) Frobenius splitting numbers of a local ring of prime characteristic are lower semicontinuous.