The Kato-Nakayama Space as a Transcendental Root Stack

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 [2] from the Kato Nakayama space to the (topological) infinite root stack.