Number Theory Seminar
Andreea Iorga
University of Chicago
Realising certain semi-direct products as Galois groups
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.
Friday April 21, 2023 at 12:00 PM in 612 SEO