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Abelian varieties over finite fields with a specified characteristic polynomial modulo $ℓ$

Joshua Holden — 2004

Journal de Théorie des Nombres de Bordeaux

We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial $P (T)$ modulo $ℓ$ . As an application we find the proportion of isogeny classes of abelian varieties with a rational point of order $ℓ$ .

Notes on an analogue of the Fontaine-Mazur conjecture

Jeffrey D. Achter; Joshua Holden — 2003

Journal de théorie des nombres de Bordeaux

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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Abelian varieties over finite fields with a specified characteristic polynomial modulo ℓ

Notes on an analogue of the Fontaine-Mazur conjecture

Abelian varieties over finite fields with a specified characteristic polynomial modulo $ℓ$