EVENT DETAILS AND ABSTRACT

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.