Christophe Ritzenthaler: Geometry and arithmetic of curves of low genus

Collection Christophe Ritzenthaler: Geometry and arithmetic of curves of low genus

The first purpose is to introduce/recall basic properties of algebraic curves in order to be able to describe precisely these curves up to genus 5. Having this geometric description will be a first step to control their arithmetic. We will then study Weil’s conjectures for curves over finite fields and various corollary: these results encode deep control on the number of rational points. In particular, we will see that they give non-trivial bounds for the number of points. The course will largely follow the attached notes to which we refer for a more detailed description of the content. As the notes already exist, the videos won’t be a rewriting of the notes on the blackboard. The lecturer will motivate the study of each chapter, clarify some difficulties (for instance by giving details on a long example), and give further connections and illustrations.


Appears in collection : CIMPA SCHOOL "Modern Tools for Rational Points on Curves over Finite Fields"


Organizer(s) CIMPA
Date(s) 15/02/2021 - 20/02/2021
linked URL https://www.cimpa.info/
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