Institut de Mathématiques de Luminy

Abstract 2001-17

Serge Vladut.
Isogeny classes and Frobenius roots statistics for abelian varieties over finite fields.

Let I(g,q,N) be the number of isogeny classes of g-dimensional abelian varieties over a finite field Fq having a fixed number N of Fq-rational points. We describe the asymptotic (for q –› ) distribution of I(g,q,N) over possible values of N. We also prove an analogue of the Sato-Tate conjecture for isogeny classes of g-dimensional abelian varieties.

 

 



Last update : september 13, 2001, EL.