Andreea Iorga : Realising certain semi-direct products as Galois groups

Posted by Alina Carmen Cojocaru , part of the Number Theory Seminar.

At

April 21, 2023, noon

In

612 SEO

Abstract

In this talk, I will show that, under a specific assumption, any semi-direct product of a $p$-group $G$ with a group $\Phi$ of order prime-to-$p$ can appear as the Galois group of a tower of extensions $H/F/E$ with the property that $H$ is the maximal pro-$p$ extension of $F$ that is unramified everywhere and $\text{Gal}(H/F) = G$. At the end, I will show that a nice consequence of this is that any local ring admitting a surjection to $\mathbb{Z}_5$ or $\mathbb{Z}_7$ with finite kernel can be written as a universal everywhere unramified deformation ring.