Tame stacks and log flat torsors

TL;DR

This paper explores the relationship between tame actions on schemes and log flat torsors on log schemes, establishing a canonical method to extend torsors into tame covers using log flat torsors.

Contribution

It demonstrates that log flat torsors provide a canonical framework for extending torsors into tame covers, connecting tame actions with log scheme torsors.

Findings

Actions underlying log flat torsors are tame.

A tame cover can be uniquely extended to a log flat torsor.

The theory offers a canonical approach to extending torsors into tame covers.

Abstract

We compare tame actions in the category of schemes with torsors in the category of log schemes endowed with the log flat topology. We prove that actions underlying log flat torsors are tame. Conversely, starting from a tame cover of a regular scheme that is an fppf torsor on the complement of a divisor with normal crossings, it is possible to build a unique log flat torsor that dominates this cover. In brief, the theory of log flat torsors gives a canonical approach to the problem of extending torsors into tame covers.