Lecturer: Christophe RITZENTHALER
Abstract
This mini-course is a motivated introduction to the problematic of number of rational points on curves over finite fields. It will serve as a pretext to introduce the basics of algebraic geometry (Nullstellensatz, projective geometry,...) with a far-away open problem in mind (distribution of the number of points on genus 4 curves). We will in particular try to reduce the number of coefficients of these curves to be able to run some experiments with a computer.