# Equimultiplicity Theory of Strongly $F$-regular rings

## TL;DR

This paper develops a unified framework for analyzing various $F$-invariants like Hilbert--Kunz multiplicity and $F$-signature over strongly $F$-regular rings, enhancing understanding of singularities.

## Contribution

It introduces techniques that unify the study of $F$-invariants and their behavior under localization in strongly $F$-regular rings.

## Key findings

- Unified approach to $F$-invariants
- Insights into singularity measurements
- Behavior of invariants under localization

## Abstract

We explore the equimultiplicity theory of the $F$-invariants Hilbert--Kunz multiplicity, $F$-signature, Frobenius Betti numbers, and Frobenius Euler characteristic over strongly $F$-regular rings. Techniques introduced in this article provide a unified approach to the study of these $F$-invariants under localization and as measurements of singularities.