Notes on an analogue of the Fontaine-Mazur conjecture
arXiv:math/0105087
Abstract
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.
12 pages; minor revisions according to referees' comments