This course addresses the study of rational points on curves over finite field. We will study them from two different points of view. On one hand, we will study how to construct curves with a given number of points and its applications, and on the other hand, we will study some statistical aspects, as the average number of points on certain families of curves.
The final grade is exclusively based on the results obtained for the weekly homework assignments.
Algebra 1, 2, 3.
Handouts of slides, partial lecture notes and research papers will be provided during the course.