# Parabolic sheaves with real weights as sheaves on the Kato-Nakayama space

## TL;DR

This paper introduces a framework for understanding parabolic sheaves with real weights on log analytic spaces by relating them to sheaves on the Kato-Nakayama space, extending previous rational-weight cases to real weights.

## Contribution

It generalizes the description of parabolic sheaves from rational to real weights by interpreting them as sheaves on the Kato-Nakayama space.

## Key findings

- Provides a new interpretation of parabolic sheaves with real weights
- Extends existing descriptions from rational to real weights
- Connects sheaves on log spaces with topological sheaf theory

## Abstract

We define quasi-coherent parabolic sheaves with real weights on a fine saturated log analytic space, and explain how to interpret them as quasi-coherent sheaves of modules on its Kato-Nakayama space. This recovers the description as sheaves on root stacks of arXiv:1001.0466 and arXiv:1410.1164 for rational weights, but also includes the case of arbitrary real weights.