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

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 .

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 .

@article{JTNB_2003__15_3_627_0,
     author = {Achter, Jeffrey D. and Holden, Joshua},
     title = {Notes on an analogue of the Fontaine-Mazur conjecture},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {15},
     number = {3},
     year = {2003},
     pages = {627-637},
     zbl = {1077.11080},
     mrnumber = {2142226},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2003__15_3_627_0}
}
Achter, Jeffrey D.; Holden, Joshua. Notes on an analogue of the Fontaine-Mazur conjecture. Journal de théorie des nombres de Bordeaux, Volume 15 (2003) no. 3, pp. 627-637. http://www.numdam.org/item/JTNB_2003__15_3_627_0/

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