Arithmetic Statistics Seminar: Realising certain semi-direct products as Galois groups

SEMINARS

Speaker:

Andreea Iorga - University of Chicago

In this talk, I will prove 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 $M/L/K$ with the property that $M$ is the maximal $p$-extension of $L$ that is unramified everywhere, and $\Gal(M/L) = G$. At the end, if time permits, 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.