Isogeny Class and Frobenius Root Statistics for Abelian Varieties over Finite Fields
نویسنده
چکیده
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. 2000 Math. Subj. Class. Primary: 11G25, 14G15, 14K15; Secondary: 11G10, 14K02, 28A33.
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تاریخ انتشار 2001