Woensdag 29 januari 2003
Vanaf half 11 is er koffie en chocola.
||Jaap Top (RUG)
||Plane quartic curves over finite fields
||11:00 - 12:00
||CK N4 (N3045)
Suppose $C$ is a smooth, plane curve given by a homogeneous equation
$F(x,y,z)=0$ of degree $n$.
In case $n<4$ it is well known (although highly nontrivial for $n=3$)
how many solutions $(x,y,z)$ such an equation can have with coordinates
in a finite field.
In the lecture we discuss the case $n=4$. In particular we will discuss upper
bounds for the number of solutions, and we will explain how to find the maximum
possible number of solutions for any field of cardinality smaller than 100.