La connexité rationnelle en arithmétique

Details La connexité rationnelle en arithmétique La connexité rationnelle en arithmétique

2010-03-08

arxiv.org/abs/1003.1659v4

Mathematics

Algebraic Geometry

63 pages; minor updates

Scientific paper

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.

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