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

2000/10/31 by Joshua Holden
Mathematics · #math.NT #math.AG

paper · pdf

published as Journal de Theorie des Nombres de Bordeaux, 16:173--178, 2004. · 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

arxiv created 2001/05/26 · arxiv updated 2009/11/30

Abstract

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.

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