The Kato-Nakayama space as a transcendental root stack

TL;DR

This paper provides a functorial framework for understanding the Kato-Nakayama space of log analytic spaces, linking it to root stacks and offering a global perspective on related comparison maps.

Contribution

It introduces a functorial description of the Kato-Nakayama space analogous to root stacks, enhancing the understanding of its structure and relation to infinite root stacks.

Findings

Provides a functorial description of the Kato-Nakayama space.

Establishes a global description of the comparison map to the infinite root stack.

Connects the Kato-Nakayama space with root stacks in a functorial manner.

Abstract

We give a functorial description of the Kato-Nakayama space of a fine saturated log analytic space that is similar in spirit to the functorial description of root stacks. As a consequence we get a global description of the comparison map constructed in arXiv:1511.00037 from the Kato-Nakayama space to the (topological) infinite root stack.