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. |