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Je présenterai des résultats de T. Ekedahl et H. Esnault sur les variétés projectives lisses sur un corps de caractéristique strictement positive, disons
p
, dont deux points peuvent être liés par une chaîne de courbes rationnelles, par exemple faiblement unirationnelles, ou de Fano. Notamment : 1) sur un corps fini, de telles variétés ont un point rationnel, résultat qui généralise le théorème de Chevalley-Warning ; 2) sur un corps algébriquement clos, de telles variétés ont un groupe fondamental...
Soit
X
un schéma projectif intègre défini sur un corps de nombres
F
; soit
L
un fibré en droites ample sur
X
muni d’une métrique adélique semi-positive au sens de Zhang. Les résultats principaux de cet article sont :
(1)
Une formule qui calcule les hauteurs locales (relativement à
L
) d’un diviseur de Cartier sur
X
comme des « mesures...
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