Tame stacks and log flat torsors

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.