# Differentials on the arc space

## TL;DR

This paper describes how to compute the sheaves of Kähler differentials for arc spaces and jet schemes directly from the original scheme's sheaf, providing new insights into their structure.

## Contribution

It introduces a method to compute sheaves of differentials on arc spaces and jet schemes directly from the base scheme, advancing understanding of their structure.

## Key findings

- Explicit formulas for sheaves of differentials on arc spaces.
- Applications to the structural analysis of arc spaces.
- Enhanced understanding of jet schemes' properties.

## Abstract

The paper provides a description of the sheaves of K\"ahler differentials of the arc space and jet schemes of an arbitrary scheme where these sheaves are computed directly from the sheaf of differentials of the given scheme. Several applications on the structure of arc spaces are presented.