# On p-power freeness in positive characteristic

## TL;DR

This paper investigates p-power freeness in positive characteristic, establishing criteria similar to semi-ampleness and applying them to three-dimensional birational geometry.

## Contribution

It introduces criteria for p-power freeness and demonstrates their application in three-dimensional birational geometry.

## Key findings

- Criteria for p-power freeness established
- Application to three-dimensional birational geometry demonstrated
- Analogues of semi-ampleness criteria developed

## Abstract

In this note, we study base point freeness up to taking p-power, which we will call p-power freeness. We first establish some criteria for p-power freeness as analogues of criteria for semi-ampleness. We then apply these results to three-dimensional birational geometry.