Notes on an analogue of the Fontaine-Mazur conjecture
Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 3, pp. 627-637.

On estime la proportion des corps de fonctions qui remplissent des conditions qui impliquent un analogue de la conjecture de Fontaine et Mazur. En passant, on calcule la proportion des variétés abéliennes (ou jacobiennes) sur un corps fini qui possèdent un point rationnel d’ordre ℓ.

We estimate the proportion of function fields satisfying certain conditions which imply a function field analogue of the Fontaine-Mazur conjecture. As a byproduct, we compute the fraction of abelian varieties (or even jacobians) over a finite field which have a rational point of order ℓ.

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Jeffrey D. Achter; Joshua Holden. Notes on an analogue of the Fontaine-Mazur conjecture. Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 3, pp. 627-637. https://jtnb.centre-mersenne.org/item/JTNB_2003__15_3_627_0/

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