Equivalence of two notions of log moduli stacks

TL;DR

This paper proves the equivalence of two different definitions of log moduli stacks, generalizes a key theorem by Olsson, and derives foundational results for algebraic log stacks similar to classical algebraic stacks.

Contribution

It establishes the equivalence between two notions of log moduli stacks and extends Olsson's theorem, providing a unified framework and new foundational results.

Findings

Proves the equivalence of two notions of log moduli stacks.

Generalizes Olsson's theorem on log algebraic stacks.

Derives fundamental results for algebraic log stacks.

Abstract

We show the equivalence between two notions of log moduli stacks which appear in literatures. In particular, we generalize M.Olsson's theorem of representation of log algebraic stacks and answer a question posted by him (\cite{Ol4} 3.5.3). As an application, we obtain several fundamental results of algebraic log stacks which resemble to those in algebraic stacks.