## EVENT DETAILS AND ABSTRACT

**Number Theory**
**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 $\mathbb{F}_q[t]$.

**Date:** Monday, April 16, 2012

**Time:** 4:00PM

**Where:** Lunt 107

**Contact Person:** Simon Marshall

**Contact email:** slm@math.northwestern.edu

**Contact Phone:** 847-467-0715

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