La connexit\'e rationnelle en arithm\'etique

TL;DR

This paper provides detailed proofs and discussions on the arithmetic properties of rationally connected varieties, focusing on theorems over finite and local fields, contributing to the understanding of their arithmetic geometry.

Contribution

It offers detailed expositions and proofs of key theorems by Kollár, Kollár and Szabó, and Esnault on rationally connected varieties over finite and local fields.

Findings

Proofs of theorems on rationally connected varieties over finite fields

Results on rationally connected varieties over local fields

Enhanced understanding of their arithmetic properties

Abstract

These expository notes discuss the arithmetic of rationally connected varieties. Detailed proofs of theorems of Koll\'ar, of Koll\'ar and Szab\'o and of Esnault about rationally connected varieties over finite fields and local fields are given. ----- Nous discutons dans ces notes l'arithm\'etique des vari\'et\'es rationnellement connexes. Des preuves d\'etaill\'ees de th\'eor\`emes de Koll\'ar, de Koll\'ar et Szab\'o et d'Esnault concernant les vari\'et\'es rationnellement connexes sur les corps finis ou locaux y sont donn\'ees.