The Inverse Galois Problem for p-adic Fields

Seminar: 
Algebra and Number Theory Seminar
Event time: 
Tuesday, January 17, 2017 - 11:15am to 12:15pm
Location: 
LOM 205
Speaker: 
David Roe
Speaker affiliation: 
University of Pittsburgh
Event description: 

Given a finite group $G$ and a field $K$, the inverse Galois problem is to determine whether there exists an extension $L$ of $K$ so that $\mathrm{Gal}(L/K) \cong G$. When $K$ is a $p$-adic field, there will be only finitely many extensions $L$ with $\mathrm{Gal}(L/K) \cong G$. We may thus refine the question by asking how many extensions exist and attempting to enumerate them. In this talk, I will describe an algorithm for counting such extensions. With any remaining time, I will discuss the enumeration problem and applications.