\documentclass[12pt]{article}
\usepackage{amsmath,mathrsfs,bbm}
\usepackage{amssymb}
\textwidth=4.825in
\overfullrule=0pt
\thispagestyle{empty}

\begin{document}
\noindent
%
%
{\bf Oliver Schnetz}
%
%

\medskip
\noindent
%
%
{\bf Quantum Field Theory over $\mathbb{F}_q$}
%
%

\vskip 5mm
\noindent
%
%
%
%
We consider the number $\bar N(q)$ of points in the projective
complement of graph hypersurfaces over $\mathbb{F}_q$ and show that the
smallest graphs with non-polynomial $\bar N(q)$ have 14 edges. We give
six examples which fall into two classes. One class has an exceptional
prime 2 whereas in the other class $\bar N(q)$ depends on the number
of cube roots of unity in $\mathbb{F}_q$. At graphs with 16 edges we find
examples where $\bar N(q)$ is given by a polynomial in $q$ plus $q^2$
times the number of points in the projective complement of a singular
K3 in $\mathbb{P}^3$.

In the second part of the paper we show that applying momentum space
Feynman-rules over $\mathbb{F}_q$ lets the perturbation series terminate
for renormalizable and non-renormalizable bosonic quantum
field theories.

\end{document}