## EVENT DETAILS AND ABSTRACT

**Number Theory**
**Title:** F_q-Local Systems on Abelian Varieties of Low p-rank

**Speaker:** Brett Frankel

**Speaker Info:** Northwestern University

**Brief Description:**

**Special Note**:

**Abstract:**

For an abelian variety $A$ with small $p$-torsion, we count the number of representations of the \´etale fundamental group of $A$ to $GL_n(q)$, where $q$ is a power of $p$. This count (for ﬁxed $n$) turns out to be a polynomial in $q$. The space of such representations is not a scheme, but does have the structure of a constructible set. We give an explicit formula for this polynomial, then state a few theorems which elucidate its features. In particular, we state a new result which generalizes to cosets a theorem of Frobenius about the number of solutions to $x^n = 1$ in a ﬁnite group.

**Date:** Monday, November 21, 2016

**Time:** 4:00PM

**Where:** Lunt 107

**Contact Person:** Yifeng Liu

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

**Contact Phone:**

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