TY - JOUR

T1 - Enumeration of certain varieties over a finite field

AU - Friedlander, John B.

AU - Shparlinski, Igor E.

PY - 2014/8/1

Y1 - 2014/8/1

N2 - Let Fqbe a finite field of q elements. E. Howe has shown that there is a natural correspondence between the isogeny classes of two-dimensional ordinary abelian varieties over Fq which do not contain a principally polarized variety and pairs of positive integers (a, b) satisfying q = a2+ b, where gcd(q, b) = 1 and all prime divisors l of b are in the arithmetic progression l ≡ 1 (mod 3). This arithmetic criterion allows us to give good upper bounds, and for many finite fields good lower bounds, for the frequency of occurrence of isogeny classes of varieties having this property.

AB - Let Fqbe a finite field of q elements. E. Howe has shown that there is a natural correspondence between the isogeny classes of two-dimensional ordinary abelian varieties over Fq which do not contain a principally polarized variety and pairs of positive integers (a, b) satisfying q = a2+ b, where gcd(q, b) = 1 and all prime divisors l of b are in the arithmetic progression l ≡ 1 (mod 3). This arithmetic criterion allows us to give good upper bounds, and for many finite fields good lower bounds, for the frequency of occurrence of isogeny classes of varieties having this property.

UR - http://www.scopus.com/inward/record.url?scp=84924777574&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2014-11999-X

DO - 10.1090/S0002-9939-2014-11999-X

M3 - Article

AN - SCOPUS:84924777574

VL - 142

SP - 2615

EP - 2623

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 8

ER -