Les conjectures de Weil : origines, approches, g\'en\'eralisations

TL;DR

This paper reviews the historical development, various approaches, and generalizations of Weil's conjectures concerning the count of solutions to polynomial equations over finite fields.

Contribution

It provides a comprehensive overview of the origins, methods, and extensions related to Weil's conjectures in algebraic geometry.

Findings

Historical analysis of Weil's conjectures

Survey of approaches to prove the conjectures

Discussion of generalizations and current status

Abstract

Je retracerai l'histoire des conjectures de Weil sur le nombre de solutions d'\'equations polynomiales dans un corps fini et quelques unes des approches qui ont \'et\'e propos\'ees pour les r\'esoudre. The Weil conjectures: origins, approaches, generalizations. I recount the history of the conjectures by Weil on the number of solutions of polynomial equations in finite fields, and some of the approaches that have been proposed to solve them.