EVENT DETAILS AND ABSTRACT

Title: Infinite class towers
Speaker: Jing Hoelscher
Speaker Info: UIC
Brief Description:
Special Note: Seminar now meets at 4 pm
Abstract:

Let $K$ be a finite separable extension of the rational function field $\mathbb{F}_q(t)$ of characteristic $p$ and let $S_K$ be the set of all infinite places in $K$. Schoof gave a condition for $K$ to admit an infinite Hilbert $(p, S_K)$-class field tower, which implies it is more likely for $K$ to admit infinite Hilbert $(p, S_K)$-class field towers if the number of ramified primes in $K/\mathbb{F}_q(t)$ is relatively large. I will give examples of function fields $K$ ramified only at one finite regular prime over $\mathbb{F}_q(t)$, which admit infinite Hilbert $(p, S_K)$-class field towers. Such a $K$ can be taken as an extension of a cyclotomic function field $\mathbb{F}_q(t)(\lambda_{\mathfrak{p}^m})$ for a certain regular prime $\mathfrak{p}$ in $\mathbb{F}_q[t]$.