Tame actions of affine group schemes and tame stacks

TL;DR

This paper compares two notions of tameness for affine group scheme actions and stacks, deriving results on inertia groups' structure in these contexts.

Contribution

It establishes a connection between two definitions of tameness and analyzes their implications for inertia groups in algebraic geometry.

Findings

Equivalence of tameness notions for group actions and stacks

Structural results on inertia groups in tame settings

Insights into the behavior of inertia groups in algebraic stacks

Abstract

We compare two notions of tameness: one introduced in [CEPT96] for actions of affine group schemes and one introduced in [AOV08] for stacks. From this comparison, we deduce results on the structure of inertia groups in these tame situations.