# Regularity of pseudomeromorphic currents

## TL;DR

This paper investigates the smoothness properties of pseudomeromorphic currents on analytic spaces and establishes their sheaf-theoretic properties, including injectivity when the space is smooth.

## Contribution

It proves that direct images of principal value and residue currents are smooth outside small sets and shows the sheaf of such currents is stalkwise injective on smooth spaces.

## Key findings

- Currents are smooth outside small sets.
- Sheaf of currents is stalkwise injective on smooth spaces.
- Provides structural insights into pseudomeromorphic currents.

## Abstract

Let $X$ be a (reduced) pure-dimensional analytic space. We prove that direct images of principal value and residue currents on $X$ are smooth outside sets that are small in a certain sense. We also prove that the sheaf of such currents, provided that $X$ is smooth, is a stalkwise injective $\Ok_X$-module.