Abelian varieties over finite fields with a specified characteristic polynomial modulo l
Abstract
Description
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.
5 pages, submitted to the Proceedings of the AMS. AMS-LaTeX format. Completely revised. Original paper had numerous references to unproved conjectures. These have been removed, but see math.NT/0105087 for proofs of some of them
5 pages, submitted to the Proceedings of the AMS. AMS-LaTeX format. Completely revised. Original paper had numerous references to unproved conjectures. These have been removed, but see math.NT/0105087 for proofs of some of them