# On the behavior of $F$-signatures, splitting primes, and test modules under finite covers

## TL;DR

This paper studies how $F$-signatures, splitting primes, and test modules change under finite covers, introducing the concept of transposability along sections of the relative canonical module to deepen understanding.

## Contribution

It extends the notion of transposability along sections of the relative canonical module, providing a comprehensive framework for their behavior under finite covers.

## Key findings

- Characterizes the behavior of $F$-signatures under finite covers
- Introduces the concept of transposability along sections of the relative canonical module
- Provides new insights into splitting primes and test modules in this context

## Abstract

We give a comprehensive treatment on how $F$-signatures, splitting primes, splitting ratios, and test modules behave under finite covers. To this end, we expand on the notion of transposability along a section section of the relative canonical module as first introduced by K.~Schwede and K.~Tucker.

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Source: https://tomesphere.com/paper/1904.10382