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Isogeny Class and Frobenius Root Statistics for Abelian Varieties Over Finite Fields
2001
Moscow Mathematical Journal
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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.
doi:10.17323/1609-4514-2001-1-1-125-139
fatcat:kfuv7vf5dfdjlgcto2c55tdkce