Introduction

1 When $m \geq 2$, $(g,r) = (0,4)$ and $k$ is an NF with certain conditions

2 When $m \geq 5$ and $k$ is an SℓF

3 When $m \geq 3$, $g = 0$ and $k$ is an FGF $\infty$

3.1 The group-theoretical reconstruction of inertia groups

3.2 The proof of the main theorem

3.3 Work in Progress